Martin Skrtel headed Liverpool into a 1-0 lead at halftime, but Yaya Toure levelled for City after goalkeeper Pepe Reina missed a cross and Martin Kelly failed to control the ball, allowing Kolo Toure to finish from close range in the 63rd minute.
Liverpool took the lead again three minutes later thanks to Luis Suarez's free kick. Skrtel then underhit a back pass toward Reina that Carlos Tevez latched on to before rounding the goalkeeper and slotting into an empty net to save a point for his team in the 80th.
City manager Roberto Mancini was frustrated at his side having conceded two goals in its opening two games of the season.
"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."
Liverpool manager Brendan Rodgers was happier with his team's display.
"We were asked a lot of questions and I thought the players were incredible," he said. "Sometimes the best team doesn't win."
At Britannia Stadium, Stoke and Arsenal played out a scoreless draw.
France forward Olivier Giroud came closest to winning the game for Arsenal in the final minute of the match, receiving the ball 40 yards from goal and lobbing goalkeeper Asmir Begovic only for the ball to land on the roof of the net.
Stoke had a goal ruled out from Jonathan Walters in the first half for offside.
Arsenal manager Arsene Wenger believes his side must improve its attack after failing to score in its first two games of the league season.
"Offensively, we still have some work to do because we missed a bit of accuracy in the final third in our movement and in our passing," Wenger said. "We are used to finding each other in the final third and there's something missing, but I still think we should have won the game 1-0."
Pulis was pleased with how Stoke performed and praised United States defender Geoff Cameron on his debut. Cameron looks set to be joined by U.S. midfielder Maurice Edu next week.
"We watched Geoff quite a few times and he's a good player," Pulis said. "He's been away in America for 10 days and only trained one day with us. We couldn't get him back as he had to get some clearance and we have to wait 10 days.
Pulis said he may look to make further signings from the U.S. after being impressed with the quality of football there.
"I was very impressed with the standard," Pulis said. "Hopefully that (Edu deal) will be completed by Monday. He's another player who's playing for the national team and there's a market out there, I think."