City recovered from conceding a sensational volley by Peter Crouch to salvage a point thanks to Yaya Toure's deflected long-range effort later in the second half, returning to the top of the standings on goal difference.
However, United can reclaim the lead and push three points clear with eight matches to go with a victory over Fulham in its game in hand on Monday.
"We won't know until the end of the season if it's a point gained," City assistant manager David Platt said.
Arsenal pulled three points clear of Tottenham in the battle for third place by beating Aston Villa 3-0, hours after seeing its north London rival draw 0-0 at Chelsea.
The result kept Spurs five points ahead of Chelsea, which is in danger of missing out on Champions League football for the first time since 2003.
Bolton marked its first match since Fabrice Muamba's on-field cardiac arrest last weekend with a 2-1 victory over Blackburn on an emotional day at Reebok Stadium to climb out of the relegation zone.
Queens Park Rangers replaced Bolton in the bottom three after a 3-1 loss at Sunderland, with French striker Djibril Cisse sent off for the visitors for the second time since his January move from Lazio.
Wolverhampton Wanderers stayed bottom after losing 2-1 at Norwich — their fourth straight loss — but next-to-last Wigan boosted its survival hopes with a surprise 2-1 win at seventh-place Liverpool, whose dire form has seen it win just once in seven games.
Everton won 2-0 at midtable rival Swansea in the other match.
While Man City's home form has been perfect, winning all 15 of its matches at Etihad Stadium, the team's away results are jeopardizing its chances of capturing a first title since 1968.
Roberto Mancini's side has won just two of its last eight away matches, allowing United to claw its way back into the title picture.
Without the injured Sergio Aguero, and with Carlos Tevez again on the bench, City struggled to dominate Stoke, which took the lead in the 59th minute with what will surely be a contender for the Premier League's goal of the season.
Crouch pounced on a headed clearance, teed himself up and volleyed a fabulous, angled shot into the far corner from 25 yards (meters).
"It's probably the best goal I've ever scored," the striker said. "I always enjoy a volley but they don't normally fly in like that."
Toure's equalizer came when his 30-yard shot ricocheted off the Stoke defender Ryan Shawcross and deceived goalkeeper Asmir Begovic, who could only parry the ball into the net.
"If we can take points like this, they will be vital," Toure said.
At the start of February, Arsenal's top-four hopes looked in serious jeopardy when the team was 10 points behind north London rival Tottenham.
However, a sensational upturn in form leaves Arsene Wenger's side favourites to claim third place, which brings an automatic entry into next season's Champions League group stage.
Kieran Gibbs and Theo Walcott scored first-half goals at Emirates Stadium and Mikel Arteta added a stunning third from a free kick for Arsenal.
"In the past month it has turned our way so we have to make sure we keep the momentum," Wenger said.
Tottenham remains without a win at Chelsea since 1990 but still left Stamford Bridge happy after keeping the Blues at arm's length in the race for Champions League qualification.
Juan Mata struck the post with a free kick for Chelsea but Tottenham shaded the match, with Gareth Bale heading an effort against the bar.
"It's going to be difficult for us now," interim Chelsea manager Roberto Di Matteo said, when asked about his team's top-four hopes.
Liverpool's faint chances of joining the race for the Champions League spots is surely over after a limp loss to Wigan, for whom Gary Caldwell scored the winner in the 63rd.
Uruguay striker Luis Suarez had cancelled out Wigan's opener from the penalty spot by Shaun Maloney.
Bolton claimed a second straight league win for the first time this season at the end of an emotionally draining week for the club after Muamba's collapse during an FA Cup match against Tottenham at White Hart Lane last Saturday.
Fans held up cards as part of a mosaic that spelt out "Muamba 6" before kickoff while there was a period of applause for the midfielder, who has recovered miraculously according to doctors after his heart stopped beating on its own for 78 minutes.
The game was settled by two first-half goals by Bolton defender David Wheater.
"The players are out on their feet physically and mentally," Bolton manager Owen Coyle said.
Bolton is a point clear of QPR and Wigan, with Wolves three points further adrift.