Manchester United needed two Paul Pogba penalties to stay in contention for a top-four Premier League finish by beating West Ham 2-1, while Tottenham moved up to third thanks to Lucas Moura's hat-trick in a 4-0 win over Huddersfield on Saturday. United had lost four of their previous five games in all competitions and were extremely fortunate to get back to winning ways as West Ham had a goal ruled out for offside, hit the crossbar and saw David de Gea make a wonder save to deny Michail Antonio giving them a late lead.
However, a much-needed win moved Ole Gunnar Solskjaer's men up to fifth, at the expense of Arsenal, and to within two points of Chelsea in fourth.
United were gifted a first-half lead when Robert Snodgrass's clumsy challenge brought down Juan Mata and Pogba sent his first spot-kick down the middle of the goal.
West Ham were deservedly level four minutes into the second half when Felipe Anderson turned home at the back post, and the visitors went on to enjoy the better of the chances.
Antonio crashed a shot from range off the bar before De Gea produced a stunning save to claw the West Ham forward's header to safety.
Within seconds of being saved by their captain, United had a second penalty 10 minutes from time when Ryan Fredericks chopped down Anthony Martial, and this time Pogba buried his penalty into the bottom corner.
Tottenham up to third
Tottenham had no such strife despite missing Harry Kane, who is expected to miss the rest of the season due to ankle ligament damage.
Dele Alli was also sidelined by a broken hand, while Mauricio Pochettino took the chance to rest some other key personnel, including Son Heung-min, ahead of the second leg of his side's Champions League quarter-final against Manchester City, with Tottenham holding a 1-0 lead in the tie.
Lucas took his chance to shine against the already relegated Terriers to show Pochettino he could be an important weapon in Kane's absence as Spurs look to tie down a top-four finish.
"Players need to play to show their quality. The hat-trick is going to build his confidence," said Pochettino.
Victor Wanyama opened the scoring on 24 minutes to allay any fears that Tottenham could suffer a Champions League hangover.
Lucas made it 2-0 three minutes later and then struck twice more in the final three minutes as Pochettino's men made it three wins from three at their impressive new 62,000-capacity home.
Controversial Cardiff defeat
While the title and fight for top-four places look set to go down to the wire, the relegation battle could be all but over should Brighton beat Cardiff on Tuesday.
The Welsh side are five points adrift of safety after a controversial 2-0 defeat to Burnley.
Chris Wood gave the hosts a merited half-time lead, but Cardiff were left furious after referee Mike Dean overruled his assistant's decision to award a penalty to the visitors after the break.
Another big Cardiff penalty appeal was turned down before Wood sealed the win in stoppage time.
Brighton remain catchable for Neil Warnock's men as they succumbed to a humiliating 5-0 home defeat to Bournemouth.
The Cherries had lost 11 of their last 12 games on the road, but moved up to 12th thanks to goals from Dan Gosling, Ryan Fraser, David Brooks, Callum Wilson and Junior Stanislas.
A dreadful day for the Seagulls was rounded off by a red card for Anthony Knockaert.
"We've got to get back to being the solid team we know we can be," said Brighton boss Chris Hughton. "If we thought today was a big game then Tuesday is an even bigger one."
Southampton further eased their relegation fears with a 3-1 win over Wolves to move eight points clear of the drop zone.
Fulham's relegation to the Championship is already assured, but they secured just a fifth win of the season by beating Everton 2-0.