The Argentinian, now firmly back in favor, seized on a backpass to strike his side's second equalizer and prevent City from slipping to their first Barclays Premier League defeat of the season.
But new manager Brendan Rodgers was denied his first league win as City again produced the sort of comeback that's becoming its specialty. Rodgers hailed his players as "incredible."
"My glass is very nearly full," he said. "I thought it was a brilliant performance. We were asked a lot of questions and I thought the players were incredible. Some times the best team doesn't win. Let's remember we were playing a good side."
After coming from behind to win its 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.
Joe Allen looking composed on his home debut but said afterward, "it was pretty frantic."
"It was a brilliant game for the neutral and it was great to go ahead twice, so we're disappointed not to win the game," Allen told Sky Sports. "Bittersweet probably sums it up perfectly."
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 Steven Gerrard twice stabbed low long-range shots wide in the opening three minutes.
Yet the game had hardly started when Liverpool was forced to make a change as Lucas, who missed most of last season with a knee injury, hobbled off after four minutes.
City had its first attempt on goal when Aleksandar Kolarov fired a free kick straight at Jose 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 Fabio 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.
"Carlos is in good form at this moment, City boss Roberto Mancini said. "I am happy for him. It is important he continues to play like he did in these two games."
Liverpool then began to establish control with Sterling particularly being 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 was stung by the goal and struggled to make an impression as Liverpool dominated the remainder of the first half.
"This is the time to finish conceding two goals every game," Mancini said. "But we have taken one point when we went down two times. We started with the ball for 30 minutes, we had it in their half and had four or five chances to score. But we conceded a goal from a corner and something changed."
The hosts went close to doubling their lead before the break as Suarez flashed narrowly wide with another effort.
The Merseysiders thoroughly deserved their halftime 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.
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 was 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 penalized for handball 25 yards from goal and Suarez stepped up to bend a low effort past an ineffective wall.
It might have gotten 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.
Rodgers cleared Skrtel of blame.
"He was brave enough to play it and that's the development of the team. As a group we will only get better," Rodgers said.
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.