Sergio Ramos gave Vicente Del Bosque's side the lead shortly into the second half but Teemu Pukki made the most of a rare chance for the visitors to draw level on 78 minutes.
The result means the World Cup holders slipped to second place in Group I and need to beat leaders France in Paris next Tuesday if they are to reclaim their place at the top of the group.
Despite Didier Deschamps' men controlling possession, it took them until first-half stoppage time to take the lead through Olivier Giroud.
But goals early in the second half from the outstanding Mathieu Valbuena and Franck Ribery put them in control before Alexander Kobakhidze got one back for the visitors.
Bastian Schweinsteiger and Mario Gotze's quickfire goals in the 20th and 22nd minutes unlocked the game for Joachim Low's men before Thomas Muller wrapped up victory for the Germans.
Kazakhstan tried to make a game of it, particularly in the second half, but the third goal knocked the stuffing out of them.
Also in Group C, Austria cruised to their second win of the qualifying campaign by crushing the Faroe Islands 6-0 in Vienna.
Needing to keep the pressure on Sweden and the Republic of Ireland - who drew 0-0 on Friday night - in Group C, Austria dominated from the off against the group minnows and were 3-0 up inside the opening 30 minutes.
Philipp Hosiner had already been denied twice by Gunnar Nielsen - the first after just 18 seconds - before grabbing an eighth-minute opener when he tucked in Christian Fuchs' cross.
Hosiner got the second as well from close range in the 20th minute before Andreas Ivanschitz made it 3-0 with a strong left-footed shot from just outside the area.
Goals from Zlatko Junuzovic, David Alaba and Gyorgy Garics completed the win.
Ten-man Montenegro maintained their two-point lead at the top of Group H after Mirko Vucinic's goal was enough to win 1-0 at Moldova.
After a poor first half from Montenegro, Milorad Pekovic saw red early in the second half, but Moldova could not hold out as Vucinic secured the victory.
Montenegro now face England - who beat San Marino 8-0 on Friday night - on Tuesday night.
Ukraine claimed their first victory in Group H by beating their Euro 2012 co-hosts Poland 3-1 on a thrilling night in Warsaw.
The visitors had failed to win a competitive game since beating Sweden at last summer's tournament but a double salvo from Andriy Yarmolenko and Oleg Gusev put them on the right track.
Lukasz Piszczek ensured a few nervous minutes when he notched Poland's only goal but Roman Zozulya made the points safe for Ukraine on the stroke of half-time.
While the win was hardly the most convincing of Oranje's impressive run it was enough to ensure they moved five points clear in Group D.
After a frustrating opening half substitute Rafael van der Vaart opened the scoring on 47 minutes before Robin van Persie and substitute Ruben Schaken sealed victory.
Alexandru Chipciu's goal in the third minute of stoppage time earned Romania a valuable 2-2 draw in their Group D clash in Hungary.
The Steaua Bucharest player, on as an 86th-minute substitute, grabbed the visitors' second leveller of the match to keep his side level on points with Hungary in second place.
Balazs Dzsudzsak's penalty in the 70th minute had looked set to give the hosts victory, coming just three minutes after Adrian Mutu scored Romania's first equaliser with a penalty of his own to cancel out Vilmos Vanczak's opener.
The draw kept Hungary above Romania on goal difference as the pair battle it out for a play-off spot
Turkey breathed life back into their fading qualifying campaign with a 2-0 victory over minnows Andorra, although it was not the goal-laden result their fans might have been hoping for.
Abdullah Avci's men have had a hugely disappointing start to qualifying, picking up just three points from their opening four games before Friday night, but a match against Group D whipping boys Andorra offered the chance for the Euro 2008 semi-finalists to begin to build some momentum.
They did get the expected victory in Andorra La Vella to double their tally, but had to settle for just the two first-half goals from Selcuk Inan and Burak Yilmaz as hosts Andorra fought hard to avoid another heavy loss.
Portugal are renowned for making hard work of supposed lesser teams in qualification and this Group F clash followed suit, with Paulo Bento's men recovering from a 3-1 deficit to stay on level terms with their hosts in the group.
Russia are the runaway leaders on 12 points - they play Northern Ireland on Saturday - with Israel then shading Portugal on goal difference only, with both sides having amassed eight points.
Israel should be clear, though, despite going behind to Bruno Alves' second-minute opener.
After that Tomer Hemed, Eden Ben Basat and Null Gershon spun things around, only for Helder Postiga and Coentrao to even things up.
In the other Group F match of the night, Luxembourg remain rooted to the bottom of the standings after a goalless draw with Azerbaijan at the Stade Josy Barthel.
Visiting goalkeeper Kamran Agayev was forced to make several fine saves although it was Azerbaijan who came closest to scoring when Pardis Fardjad-Azad saw his header come back off a post.
Croatia claimed a comfortable 2-0 win over Serbia as the grudge Group A match in Zagreb ended in handshakes.
For such a potentially incendiary fixture, bust-ups and bone-crunching challenges were conspicuous by their absence as players and staff alike kept their heads.
Mario Mandzukic put Croatia in front midway through the first half and Ivica Olic made it two at the break, with Serbia offering more in the second half but ultimately coming up short.
Belgium lead the way in Group A on goal difference after a comfortable 2-0 win in Macedonia.
Kevin De Bruyne and Eden Hazard with a penalty were on target for the visitors, who are now on 13 points from five matches and a goal better off then Croatia.Wales won 2-1 at Scotland in Friday night's other Group A game.
Tottenham midfielder Gylfi Sigurdsson scored both goals to sink Slovenia and keep Iceland's hopes of World Cup qualification alive with a 2-1 victory.
Sigurdsson struck the winner in the 78th minute with a right-foot shot from the centre of the penalty box after being played in by former Chelsea veteran Eidur Gudjohnsen.
The three points take Iceland on to nine in Group E and they were a just reward for their perseverance after a niggly match littered with fouls.
Milivoje Novakovic, Slovenia's 33-year-old spearhead who plies his trade in Japan's J League with Omiya Ardija, had put the hosts ahead in the first half.
Norway have slipped to fourth place in Group E after suffering a 1-0 home defeat to Albania.
Hamdi Salihi's 67th-minute strike proved to be the only goal of the contest in Oslo.
The visitors were reduced to 10 men in the closing stages after Andi Lila picked up two bookings in quick succession, but their opponents were unable to salvage anything from the game.
Three second-half goals guided Denmark to a comprehensive 3-0 victory over the Czech Republic as they claimed the first win of their qualification campaign.
The hosts had the better of the first half before Denmark took control towards half-time and they were on top thereafter.
Denmark's superiority was rewarded with goals by Andreas Cornelius, Simon Kjaer and Niki Zimling moving them on to five points in Group B, the same as their hosts although still five behind leaders Italy.
In the night's other Group B game, Aleksandar Tonev scored a hat-trick as Bulgaria beat Malta 6-0 in Sofia.
The Lech Poznan forward scored twice in the first half to put the hosts in command before Ivelin Popov got a third just after the break.
Emil Gargorov made it four and Tonev completed his treble before Ivan Ivanov rounded off the scoring.
Edin Dzeko scored twice as Bosnia-Herzegovina brushed aside Greece 3-1 in Zenica to move three points clear in Group G.
Manchester City striker Dzeko opened the scoring in the 30th minute and made it 3-0 with his second eight minutes after half-time to all but wrap up the points for the hosts.
In between those two efforts Vedad Ibisevic also got his name on the scoresheet, following up to score after Zvjezdan Misimovic had seen his 35th-minute penalty parried by Greek goalkeeper Orestis Karnezis.
Greece managed to pull a late goal back through Theofanis Gekas, but it was not enough to prevent them losing their unbeaten record in Group G and a share of top spot.
Lithuania ground out a creditable 1-1 draw in Zilina to deny Slovakia a share of second place in Group G.
Slovakia quickly cancelled out Darvydas Sernas' opener but, despite their dominance all over the pitch, a header from Jan Durica was the sum total of their efforts.
Latvia missed a penalty as Liechtenstein claimed their first point in Group G.
Michele Polverino's opener briefly had Liechtenstein on track for a first World Cup win since 2005 but Aleksandrs Cauna's free-kick dragged Latvia back into the tie.
The same player saw his second-half penalty saved, however, and Latvia stay fifth in the group behind Lithuania and Slovakia after the 1-1 draw.