Premier League table topper Manchester City restored a six-point lead after a lucky escape at Everton, while its cross-town rival United was held by the lowly Watford on Saturday.
Phil Foden struck the only goal in the 82nd minute to break Everton's resistance but City breathed a sigh of relief when Rodri got away with a handball soon after with video assistant referee (VAR) failing to award Everton a penalty.
Manchester United's top-four hopes were dented as it was held to a 0-0 draw by relegation-threatened Watford.
Denmark international Christian Eriksen made an emotional return to competitive action as a substitute for Brentford, eight months after suffering cardiac arrest at Euro 2020.
But Brentford went down 2-0 at home to Newcastle United as its transformation continued under manager Eddie Howe.
Leeds United's slide continued as it suffered a 4-0 home loss by a Harry Kane-inspired Tottenham Hotspur.
With Liverpool playing in Sunday's League Cup final against Chelsea, Man City knew only victory against Everton would keep the title race in its own hands.
With Everton repelling City, it seemed that Pep Guardiola's side was about to open the door wide open for Liverpool, but Foden pounced late on to turn in Bernardo Silva's cross.
City moved to 66 points from 27 games with Liverpool on 60 having played 26 games. The two sides meet at the Etihad Stadium in April.
"We were searching. We tried and we were there. We earned the good fortune. Everton has top players. Their quality is there, we knew it," Guardiola said.
Everton is now only one place and one point above third-from-bottom Burnley who completed a good week with a 1-1 draw with Crystal Palace at Selhurst Park.
Burnley has 21 points with Everton on 22, both teams having played 24 games. Leeds has 23 points in 16th place and has played two games more while Brentford has 24 but has played three games more than Burnley and Everton.
Watford, in 19th place, has 19 points after battling for a point at Old Trafford.
Cristiano Ronaldo hit the post in the fifth minute and had an effort disallowed for offside but United struggled to create enough clear-cut chances against Roy Hodgson's side.
Bruno Fernandes was unable to convert two good opportunities in the first half and Anthony Elanga was off target with the best opportunity after the break.
United remains fourth but is only two points above Arsenal who has three games in hand.
"We did everything apart from score. It's hard to take that result," said United's interim manager Ralf Rangnick.
"We need to be sharper in front of goal, you can hardly create more chances than we did today."
Eriksen's return to a football pitch was a happy moment in a bleak weekend for news but he could not inspire a Brentford comeback after coming on as a substitute.
"If you take away the result. I'm one happy man. To go through what I've been through, being back is a wonderful feeling," said the Dane.
Brentford had Josh Dasilva sent off after 11 minutes for a bad tackle and Newcastle took advantage with Joelinton and Joe Willock scoring before halftime as Newcastle climbed up to 14th place, having been bottom only three weeks ago.
Leeds fell apart at Elland Road as Matt Doherty and Dejan Kulusevski put Spurs in the driving seat inside 15 minutes.
Kane volleyed home a third in the 27th minute, making Leeds only the second side in Premier League history to concede three or more goals in five consecutive matches in the competition after Sunderland in November 2005.
Son Heung-min completed the route late on.
Burnley earned a point at Palace as home defender Luka Milivojevic turned a drive from Aaron Lennon into his own net.
Aston Villa won 2-0 at Brighton & Hove Albion thanks to goals from Matty Cash and Ollie Watkins.
Many players showed their support for Ukraine as the Russian invasion continues. At Goodison Park, Everton's team walked out draped in Ukraine flags while Man City's players wore T-shirts emblazoned with "No War" slogans.
