Sergio Aguero's 79th-minute equalizer earned City a scarcely deserved point that will be of little comfort to manager Roberto Mancini, whose team has now dropped four points in six days and is struggling to keep pace with United's relentless form.
"Seven or nine points doesn't change (anything), I think we can recover it," Mancini said.
Tottenham beat West Bromwich Albion 1-0 in the other game thanks to another superb goal from star winger Gareth Bale, and is now just a point behind third-place Chelsea.
The game turned on the sending-off of West Brom defender Goran Popov in the 48th minute for spitting in the direction of Spurs right back Kyle Walker, with Bale scoring 19 minutes later.
"I'm absolutely disgusted with Goran's behaviour," West Brom manager Steve Clarke said. "There's no excuse for that. There's no place for it in life, never mind on a football pitch."
Liverpool stayed seventh — nine points behind Spurs and six adrift of local fifth-place Everton, which occupies the league's sole Europa League spot — and is still awaiting a victory over a team in the top half of the table this season.
But after a draw at Arsenal on Wednesday and another point at City, Liverpool is gathering momentum ahead of some easier games in the run-in.
"We have come to the home of the champions and dominated," Liverpool manager Brendan Rodgers said, "(but) we know we can be better."
City produced one of its poorest performances at home this season and couldn't cope with the pace and movement of Liverpool forwards Daniel Sturridge and Luis Suarez.
Sturridge — a recent signing from Chelsea — stood out, cancelling out Edin Dzeko's 23rd-minute opener with a fiercely struck equalizer six minutes later and causing havoc with the home defence.
"I feel like I am maturing a bit, getting a bit fitter," said Sturridge, who nevertheless finished the match with strapping around his left thigh.
Steven Gerrard rifled home a dipping volley in the 73rd to leave City on the brink of only its second home loss this season, but Aguero came to the rescue by running onto Gareth Barry's cross, rounding goalkeeper Pepe Reina and finding the net from an acute angle.
"In the last month we played well in all the games but we were so nervous in this game and I don't know why," said Mancini, who was missing injured captain Vincent Kompany and key midfielder Yaya Toure.
Popov's straight red card was set to provide the major talking point at the Hawthorns before Bale took centre stage, drifting inside and smashing home a swerving shot from outside the area for his 11th goal of the campaign.
It was the second superb goal he has scored this week, after his solo strike in a 1-1 draw at Norwich on Wednesday when he ran 60 yards before finding the net.
"I am enjoying my football at the moment, and when I am doing that, I usually play well," Bale said.
Tottenham is now within reach of Chelsea, which lost 3-2 at Newcastle on Saturday.