Liverpool's slim title hopes took another huge blow with a 2-2 draw at West Ham United on Saturday, while bottom team Sheffield United's relegation was confirmed with a 5-1 thrashing at Newcastle United on a pivotal day in the Premier League.
Everton confirmed their survival from relegation with a 1-0 win over Brentford, while the Bees are also safe thanks to Luton Town's 2-1 loss to Wolverhampton Wanderers.
Chelsea came back from two goals down to draw 2-2 with Aston Villa, threatening Villa's Champions League hopes, while Manchester United could muster only a 1-1 draw against Burnley after conceding a late penalty and Crystal Palace salvaged a 1-1 draw at Fulham.
Liverpool, reeling from a 2-0 loss at Everton on Wednesday, conceded a late header by Michail Antonio in West Ham's deserved draw. They remained third on 75 points, one behind second-placed Manchester City, who have played two games fewer, and two behind leaders Arsenal, who have a game in hand. Both City and Arsenal play on Sunday.
Asked if he had written off Liverpool's title chances, a resigned-looking manager Juergen Klopp said: "I said before we need to win our games; we didn't win the game, that doesn't improve our situation massively.
"Do they (City and Arsenal) look like they will lose two or three games? No, I don't think so."
Klopp's side conceded first when Jarrod Bowen nodded home shortly before halftime. The Reds levelled after the restart through Andy Robertson and then Cody Gakpo put them ahead in the 65th minute, before Antonio levelled when he met Bowen's cross with a powerful header in the 77th.
Liverpool's game was marred by a heated exchange between Klopp and talisman Mohamed Salah when he was substituted on late in the game.
"We spoke about that in the dressing room and it's done for me, that's all," Klopp told reporters.
Salah, however, told reporters that "there's going to be fire today if I speak", in footage uploaded to social media.
Idrissa Gueye's strike on the hour mark secured Everton a spot in the Premier League next season. Sean Dyche's 15th-placed Everton have 36 points, 11 ahead of 18th-placed Luton. Brentford fell to 16th but their 35 points mean they are safe as well.
"Incredibly pleased and proud. They're a group of players who have had knocks all season," Dyche said. "They've had a massive week. There's a lot of pressure and intensity on the week and can you do it again?"
Conor Gallagher's brilliant strike in the second half secured Chelsea's draw at Villa Park.
Villa are fourth and seven points ahead of Tottenham, but Spurs have three games in hand. Chelsea are ninth on 48 points.
The home side went ahead 2-0 after Marc Cucurella's own goal in the fourth minute and Morgan Rogers's strike just before the break.
Late Chelsea goal disallowed
Villa were forced to replace keeper Emi Martinez with Robin Olsen at the break due to a hamstring injury but the Swede was powerless to stop Noni Madueke from pulling back a goal before Gallagher's stunning 81st-minute equaliser. Chelsea were denied a late winner from Axel Disasi after a VAR review.
"We are gutted," Gallagher said. "Quite a poor first half, just too slow on the ball. Second half was brilliant and we come back, I felt we should have won the game.
"The goal at the end should have counted but it is not my decision. We can hold our heads high and take a lot of confidence from that."
A sizzling left-footed finish by Jeffrey Schlupp got Crystal Palace a late equaliser at Fulham.
Fulham remained 13th, three points ahead of Palace, who are unbeaten in their last four matches.
Schlupp's goal cancelled out a 52nd-minute headed goal from Rodrigo Muniz.
"It was a fully deserved point," Palace manager Oliver Glasner said. "This group, these players, they came back again and never gave up."
Manchester United looked to be heading for victory after Antony's goal in the 79th minute. But substitute Zeki Amdouni scored a penalty eight minutes later after United keeper Andre Onana hit him while attempting to clear the ball.
The draw left United in sixth but six points behind fifth-place Tottenham, who have two games in hand.
"Over many phases of the game we did very good (but) we gave it away again at the end," United's beleaguered manager Erik ten Hag said. "We have to look in the mirror."
The draw was a big result for Burnley, who are 19th but kept alive their survival hopes.
"More than performance, it's the effort," said manager Vincent Kompany. "A lot of people will talk about style of play but it's useless and worthless if you don't have what they showed out there, the sacrifice for each other."
Wolves moved to 10th in the standings thanks to goals by Hwang Hee-chan and Toti Gomes, while struggling Luton remain 18th with three games to go.
Alexander Isak netted twice while Bruno Guimaraes and Callum Wilson were also on target in Newcastle's rout of Sheffield. Ben Osborn also scored an own goal for seventh-placed Newcastle, who move to 53 points from 34 games this season.
"We have not been good enough," Sheffield manager Chris Wilder said. "The league has been too powerful for us right the way through the season."