Toby Alderweireld gave Tottenham a late 2-1 win over Arsenal as Jose Mourinho's men climbed above their north London rivals, while Bournemouth kept their survival hopes alive with a chaotic 4-1 victory against Leicester on Sunday.
Mourinho had endured a barrage of criticism as Tottenham slipped out of the race to qualify for the Champions League with just one win in three games.
But thanks to Alderweireld's winner with nine minutes left, Tottenham took the local bragging rights and got back in contention for a place in next season's Europa League.
Tottenham are eighth, two points above ninth placed Arsenal and two behind Sheffield United as they try to avoid missing out on European action for the first time since 2009-10.
"We are happy because we made the fans happy, we are happy because we are still in the fight to win a Europa League position," Mourinho said.
"To be honest, Mikel (Arteta) found a way for them to play, to be stable and to improve. We felt that we should adapt slightly to them and we did it very well."
In the first north London derby at the new Tottenham Hotspur Stadium, Alexandre Lacazette put Arsenal ahead in the 16th minute with a stunning long-range strike.
Arsenal's lead lasted just three minutes as Sead Kolasinac's sloppy pass was intercepted by Son Heung-min, who eluded David Luiz before chipping over Emiliano Martinez.
In the 82nd minute, Belgian defender Alderweireld rose above a cluster of Arsenal players to meet Son's corner and plant his header past Martinez.
Arsenal could miss out on Europe entirely and boss Arteta said: "We give them a goal again and we concede a set-piece and at this level, you cannot do it."
At Dean Court, Leicester scored after 23 minutes as Jamie Vardy bagged his 23rd league goal of the season to extend his lead in the Golden Boot race.
But Bournemouth were handed a lifeline when Leicester imploded during two minutes of mayhem.
In the 66th minute, Leicester keeper Kasper Schmeichel booted a goal-kick into Wilfred Ndidi's back, forcing his team-mate to trip Callum Wilson.
Junior Stanislas stepped up to score the resulting penalty and 101 seconds later Dominic Solanke's weak shot trickled under Schmeichel's woeful attempt to save.
Leicester defender Caglar Soyuncu sent off for kicking Wilson as he attempted to retrieve the ball from the net after Solanke's goal.
Bournemouth's luck was in and Stanislas's strike went in off Leicester's Jonny Evans for an 83rd minute own goal before Solanke's composed finish made it four in the 87th minute.
Bournemouth's first win in 10 games, a drought stretching back to February 1, moved them to within three points of 17th placed Watford, with three games left for all the teams in the relegation fight.
Cherries boss Eddie Howe said: "The situation was as bleak as it could be at half-time. But goals always change games.
"It was probably the first time in a long time where we've had some luck. We can still survive."
Fourth placed Leicester will drop to fifth if Manchester United beat Southampton on Monday, leaving their hopes of Champions League qualification in danger.
"I didn't see that coming but we are not good enough to get too comfortable. We will finish where we deserve to," Leicester manager Brendan Rodgers said.
Second bottom Aston Villa also boosted their survival bid with a vital 2-0 win against Crystal Palace.
Dean Smith's side kicked off at Villa Park languishing seven points from safety, but Egypt winger Trezeguet scored twice to keep them in with a chance of staying up.
Palace striker Christian Benteke was sent off for violent conduct after the final whistle.
Villa's first win in 11 league games left them four points behind Watford.
Wolves stayed in the Champions League hunt, climbing to sixth place after a 3-0 win against Everton.
Raul Jimenez's penalty and Leander Dendoncker's header out Wolves two up before Diogo Jota was gifted the third by keeper Jordan Pickford's blunder.