Joleon Lescott's own goal cancelled out Vincent Kompany's effort as 10-man Manchester City restored their five-point lead at the top of the Premier League.
Mario Balotelli was sent off for two yellow cards in the space of 18 minutes after coming on as a substitute.
But City, who dropped points for the second time this term, held on to draw.
Liverpool's Wales forward Craig Bellamy was left out following the death of Gary Speed.
Reds manager Kenny Daglish took the decision to send the striker home.
He said: "It was best for us to make the decision for Craig. He was very close to Gary, who was a mentor to him, and he admired and looked up to him."
On Roberto Mancini's 47th birthday, City had the opportunity to take advantage of second-placed Manchester United's 1-1 draw with Newcastle on Saturday to move seven points clear at the top of the table.
They deserved their lead after Kompany headed in, only for Lescott to divert Charlie Adam's shot into his own net less than two minutes later.
But after Balotelli was shown a second yellow card with seven minutes left, City were grateful to cling on for a point.
Initially City coped well with Liverpool's high-tempo pressing game and Yaya Toure went close to giving the visitors an early lead when he thumped a shot just past the top corner after the Reds struggled to clear Samir Nasri's corner.
Liverpool goalkeeper Jose Reina also had to be alert as he rushed out to get to Jose Enrique's weak back-pass ahead of Sergio Aguero.
Just after the half hour, the leaders were rewarded for their quiet authority when David Silva's corner picked out Kompany's near-post run and the ball glanced off the Belgian's shoulder and into the top corner.
Liverpool had still not managed an effort on target but their response was almost immediate and they drew level when Adam's shot, which looked like it was going well wide, deflected off Lescott and past Joe Hart.
The hosts continued to pile forward and Hart did well to turn away Adam's low drive with his foot before Glen Johnson curled wide from just outside the area.
City cut through once again when Aguero exchanged passes with Silva and his stabbed effort was blocked at the near post by Reina.
After the restart Nasri drove a cross-shot past Reina's post and at the other end Dirk Kuyt headed wide from Stewart Downing's cross.
When City failed to spot Adam taking a short corner to Daniel Agger, the Dane crossed for Downing and the former Middlesbrough man's strike was turned over the bar by Hart.
But after coming on as a substitute, Balotelli was shown a second yellow card after catching Martin Skrtel with an elbow, his third dismissal since joining from Inter Milan in the summer of 2010.
As the hosts pressed for a winner, Hart turned Suarez's drive around the post before Silva had the chance to steal it for City after a quick breakaway.
Hart also pulled off a fine double save from Andy Carroll and Suarez deep in stoppage time.
Liverpool manager Kenny Dalglish:
"Their keeper had a few good saves and that's what he's there for but we're delighted with the performance the boys put in, with fantastic attitude, commitment and determination and pride in playing for the football club.
"We've played both Manchester clubs here and we're disappointed only to have got one point from each, which is a mark of the improvement we've made.
"I suppose it's an unbeaten run but we don't count backwards, we look forwards and we're delighted with the way the team is playing because it's in its infancy."
Manchester City manager Roberto Mancini:
"We showed strong character because it is very difficult to play here against Liverpool and also because we tried to win, we played well and only in the last 10 minutes we conceded three or four chances but Joe [Hart] saved well.
"For me the second one was not a yellow card [for Balotelli]. I don't think that the referee wanted to give a yellow card but the Liverpool players said something.
"We conceded two or three chances when we were down to 10 men but we had a good result."