Skrtel (34) put the Reds ahead at half-time with a thumping header from Steven Gerrard's corner, only for Yaya Toure to equalise from Carlos Tevez's cross on 63 minutes.
However, three minutes later, Luis Suarez restored Liverpool's lead with an excellent free-kick curled around the City wall.
But Skrtel's blind backpass on 80 minutes gifted Tevez the opportunity to reound Pepe Reina and score, and the Argentinian made no mistake as he netted his 100th goal in English football to give the champions a point.
Liverpool were much improved after crashing 3-0 at West Brom in their opener, but new manager Brendan Rodgers was denied his first league win as City again produced the sort of fightback they are beginning to specialise in.
After coming from behind to win their last three games 3-2, a City side which showed five changes had to settle for a draw this time.
Liverpool dominated for large spells with 17-year-old striker Raheem Sterling impressing on his first league start and Joe Allen looking composed on his home debut.
Mario Balotelli partnered Tevez up front for City on his first start since being sent off at Arsenal last April - and on a ground where he was dismissed last year - but despite looking focused, had a quiet game.
Liverpool showed early intent as captain Gerrard twice stabbed low long-range shots wide in the opening three minutes.
Yet the game had hardly started when Liverpool were forced to make a change as Lucas, who missed most of last season with a knee injury, hobbled off after four minutes.
City had their first attempt on goal when Aleksandar Kolarov fired a free-kick straight at Reina before Pablo Zabaleta launched a counter-attack with a fine tackle on Fabio Borini. Tevez took up the attack but his cross found no-one.
Liverpool should have gone ahead when the lively Sterling whipped in a fine cross for Borini but the Italian volleyed wide.
Tevez almost made him pay instantly as he latched on to a well-weighted pass from Samir Nasri and rounded Reina but the angle was too tight and he did well enough to hit the far post.
Kolo Toure tried his luck with a long-range shot but Skrtel blocked and a free-kick on the edge of the area came to nothing after Balotelli robbed Sebastian Coates and was tripped by Martin Kelly.
Liverpool then began to establish control with Sterling particularly looking a handful.
Kolo Toure blocked an effort by Borini, Suarez curled wide and City captain Vincent Kompany almost sliced a vicious low curling cross from Gerrard into his own net.
The Reds were not to be denied any longer as Skrtel came forward for the resulting corner and powered a header past Joe Hart from Gerrard's cross.
City were stung by the goal and struggled to make an impression as Liverpool dominated the remainder of the first half.
The hosts went close to doubling their lead before the break as Suarez flashed narrowly wide with another effort.
The Merseysiders thoroughly deserved their half-time lead and ovation and returned with much the same enthusiasm as Borini pounced on a mistake to set up Suarez, but the Uruguayan missed the target.
City boss Roberto Mancini began to make changes around the hour as he sought a way back into the game. Former Everton man Jack Rodwell predictably entered to boos from the home fans when he replaced Nasri and Edin Dzeko came on for Balotelli.
Within moments, City were back level, but it owed much to defensive mistakes.
Tevez beat Sterling on the right and fired in a cross which the outstretched Reina was unable to claim. Kelly was wrong-footed by the Spaniard's attempts to gather and could not prevent the ball bouncing off him into the path of Yaya Toure, who swept home from close range.
Liverpool did not dwell on the disappointment and produced the perfect response.
Rodwell was penalised for handball 25 yards from goal and Suarez stepped up to bend a low effort past an ineffective wall.
It might have got worse for City as Glen Johnson charged into the area and went down but Kolarov was deemed to have made a clean tackle.
Yet just as it seemed Liverpool had the measure of the champions, Skrtel gifted them a way back into the game as Tevez seized on his poor pass back and calmly beat Reina.
Liverpool still wanted all three points and Jonjo Shelvey shot over from distance before Andy Carroll came on to a huge roar in the closing minutes.
City also pushed forward and Dzeko twice missed the target with shots.
Carroll almost grabbed a last-gasp winner as he got his head to a Suarez cross but Kompany headed off the line.