Watford were relegated from the Premier League following defeat at Crystal Palace, while Burnley's survival bid suffered a setback after losing at home to Aston Villa.
The Hornets needed to win to avoid following Norwich straight back to the Sky Bet Championship, but were beaten 1-0 at Selhurst Park in a game they finished with 10 men.
Wilfried Zaha put the Eagles ahead from the penalty spot in the 31st minute for his 14th goal of the season.
Watford had defender Hassane Kamara sent off for a second yellow card with 20 minutes left as they dropped back down after just one campaign in the top flight.
Burnley had pulled themselves out of the relegation zone following an upturn in fortunes under interim boss Mike Jackson – but will be looking anxiously over their shoulder again after Villa ran out comfortable 3-1 winners at Turf Moor.
Danny Ings set Villa on their way after seven minutes, before Emi Buendia doubled the lead with a deflected effort just after the half-hour.
Burnley had defender James Tarkowski forced off by injury early in the second half, and fell further behind when Ollie Watkins headed in Villa’s third after 52 minutes.
Substitute Maxwel Cornet scored a stoppage-time consolation goal for Burnley, who remain 16th, two points clear of Everton – but having now played two matches more.
Chelsea saw Wolves fight back to draw 2-2 at Stamford Bridge, where prospective new owner Todd Boehly was watching on.
Ruben Loftus-Cheek and Timo Werner both saw first-half efforts ruled out, before Romelu Lukaku did put Chelsea ahead from a 56th-minute penalty.
The Belgium forward quickly added a second to double the Blues’ lead just two minutes later.
Francisco Trincao fired in a fine 18-yard effort to drag Wolves back into the match with 11 minutes left.
And there was more late drama when Conor Coady headed in an equaliser deep into stoppage time to earn Wolves a point.
Brentford, the only of the promoted sides set to stay up, saw off Southampton 3-0.
Bees captain Pontus Jansson broke the deadlock after 13 minutes and the home side doubled their advantage just seconds later through Yoane Wissa.
Southampton midfielder Adam Armstrong saw his smart finish ruled out for offside towards the end of the first half.
Defender Kristoffer Ajer scored Brentford’s third with 11 minutes left, his first goal for the club since signing from Celtic during the summer.