Aston Villa and Chelsea won home games and strengthened their hopes for a top five Premier League finish and a place in next year's Champions League.
Ezri Konsa and Boubacar Kamara scored and gave Villa a 2-0 win over an under-strength Tottenham Hotspur, and Chelsea overcame a stuffy Manchester United 1-0 thanks to a second-half goal from Marc Cucurella.
The result left Chelsea in fourth with 66 points, and Villa in fifth on goal difference.
The other teams fighting for one of the four Champions League spots after league winner Liverpool all have two games left to play.
Arsenal has 68 points, Newcastle 66, Manchester City 65, and Nottingham Forest 62.
On a tense night at Villa Park, the home side had the better of the play but was forced to wait until the 59th minute to get the opener.
Ollie Watkins steered John McGinn's corner back across goal and an unmarked Ezri Konsa turned in the ball.
Boubacar Kamara doubled the lead with a low drive from the edge of the penalty area. It was his first Premier League goal in his 69th game.
“We knew today was a must win,” the Frenchman told broadcaster Sky Sports. “We want to play Champions League football again. … We had a taste of it this season and us as players it's a competition you want to play in.”
Villa's final match is against Man United at Old Trafford on May 25.
Friday's win was Villa's eighth in its last nine league matches and extended its unbeaten home run to 21 games in all competitions, its best since 1977.
Meanwhile, at Stamford Bridge, Chelsea woke up after a dull first half when Spanish defender Cucurella headed home Reece James' cross after 71 minutes.
Spurs and Man United went into the matches with one eye on next week's Europa League final.
Both coaches rested some regular starters and got through the night without any new injury worries.
Both of Friday's matches were brought forward by 48 hours to allow the sides more time to prepare for the final on Wednesday in Bilbao.
