City coach Pep Guardiola said it was "one of the happiest days of my career as a manager" after seeing his team fight back to salvage a point against a direct rival for the top four.
Guardiola said his players had been "so, so sad" in training this week after City's elimination from the Champions League by Monaco on Wednesday.
A defeat to Liverpool four days later would have been particularly damaging to morale.
James Milner, a former City player, put Liverpool ahead from the penalty spot in the 51st today and both teams spurned great chances in a riveting final 20 minutes as they went on all-out attack.
City needed a 69th-minute equaliser from Sergio Aguero to prevent Liverpool from collecting a sixth win this season over a rival from the top six.
The move was slickly executed, with Kevin De Bruyne delivering a teasing low cross from the right that Aguero tucked home from just outside the six-yard box.
Aguero has scored in all five homes games against Liverpool in the Premier League.
In an end-to-end final 20 minutes, De Bruyne struck a shot against the post, Adam Lallana kicked fresh air from close range with the goal at his mercy, and Sterling missed a one-on-one chance.
Possibly the best opportunity fell to Aguero in injury time, but he volleyed over from close range.
A draw was probably a fair result in the end, keeping the teams in the last two Champions League qualifying places.
Liverpool kept up its excellent record against their rivals in the top six this season, with Klopp's team winning five and drawing five from 10 games. How the Reds regret slipping up so often against the league's lower-placed side.
"There is one outstanding, consistent side this year and they will be champions probably," Klopp said. "The rest fight with all they have for the Champions League."
Fourth-placed Liverpool are four points ahead of fifth-placed Manchester United, having played two games more.
The race for Champions League qualification is going down to the wire.