First-half chances were scarce for both sides but Germany appeared to have found their flow just minutes into the second as Mario Gotze stooped to bundle home Thomas Muller's inviting cross, heading it against his own knee and beyond Fatau Dauda to break the deadlock.
However, their lead lasted little more than two minutes as Ghana soon hit back when Harrison Afful's pin-point cross from the right was met by the leaping Andre Ayew who powered it beyond Manuel Neuer.
Kwesi Appiah's men were growing in confidence and they took the lead nine minutes later as Sulley Muntari's through ball took Mats Hummels out of the game and Asamoah Gyan raced free to fire past Neuer.
Joachim Low looked to change the flow of the clash as he introduced Bastian Schweinsteiger and Klose with around 20 minutes remaining, and it was the latter who made an instant impact as he turned in Benedikt Howedes' flick-on from close range following a Toni Kroos corner.
Conditions were tough for both sides ahead of the game, with humidity levels rising as high as 61 per cent amid temperatures of 29 degrees in Fortaleza.
Germany were the strong favourites ahead of kick-off, but it was Ghana who threatened first as Gyan blazed over the bar from inside the area before Christian Atsu tested Neuer from range.
Low’s side worked themselves into a number of promising positions but were unable to capitalise as the stern Ghana defence stood firm.
Mesut Ozil and Muller were finding themselves in promising positions out wide as their crosses lacked a killer touch, while Sami Khedira, Gotze and Kroos were all reduced to unleashing from distance.
Jonathan Mensah poked an effort inches wide in a lively end to the first half after some frantic German defending left Low's side relatively pleased to go into the break all square.
Much like the start of the first half, proceedings began somewhat slowly after the restart, but an inventive cross from Muller opened up the Ghana defence for the youngest member of Germany's starting line-up, Gotze, to put them ahead.
With their 4-0 victory over Portugal still fresh in the minds, questions may have been asked as to how many Ghana might ship, but Appiah's side had different ideas.
Knowing their World Cup future depended on it, they chose to attack a Germany defence which remains their Achilles heel, succeeding in levelling the match after just three minutes.
A sweeping cross from the right was met by the committed Ayew, who beat German substitute Shkodran Mustafi in the air and guided the ball beyond the reach of Neuer.
Ghana continued to push men forwards, catching Germany somewhat by surprise, and taking a deserved lead in the 63rd minute.
AC Milan midfielder Muntari disected the Germany defence with a killer pass into the path of Gyan, who raced through and provided a composed finish into the far corner of Neuer's goal.
Germany were forced to chase the game, and who better than Klose to come on and level matters, like he did in the 71st minute when he stretched to ensure Howedes' goalbound header found the back of the net.
It was the 15th World Cup goal for Klose, taking him level with Brazil's Ronaldo in the all-time World Cup scoring charts and onto a record-breaking 70 for his country.
It was also enough to earn Germany a point with some near misses at both ends late on.