Chelsea secured their place in the Champions League next season with victory over Watford at Stamford Bridge.
The win, combined with Arsenal's draw against Brighton, means the Blues are guaranteed a top-four finish in the Premier League.
After a quiet first half, Chelsea scored twice within three minutes early in the second period through headers by Ruben Loftus-Cheek and David Luiz.
Gonzalo Higuain sealed the points with a neat finish from Pedro's pass for his fifth goal for the club.
The win moves Chelsea up to third, one point ahead of Tottenham and four points clear of the fifth-placed Gunners.
FA Cup finalists Watford started brightly, going close through Troy Deeney and Gerard Deulofeu, but were left to rue their slow start to the second half that saw Chelsea quickly take the game away from them.
The Hornets, who stay 10th, have now won just one of their past five Premier League games since their FA Cup semi-final victory over Wolves last month.
Chelsea's Europa League semi-final against Eintracht Frankfurt is finely poised at 1-1 after the first leg, but Maurizio Sarri could not afford to rest players as he looked to maintain their push for a top-four finish.
The Chelsea boss says that he wants to treat all his remaining games "with the same importance".
It is a delicate balancing act for the Italian, who said he left Eden Hazard out of the starting line-up in Frankfurt on Thursday to keep him fresh for their bid to qualify for the Champions League.
Despite the presence of the influential Belgian against Watford, Chelsea began the game sluggishly, with their only shot in target in the first half a chip from Jorginho that was awkwardly palmed away by Ben Foster.
Chelsea also suffered a blow early on when N'Golo Kante was forced off through injury and had to be replaced by Loftus-Cheek.
There was a smattering of boos from the home fans at the half-time whistle. But whatever Sarri said at the break had the desired effect as his side scored two quick-fire goals to take command of the game.
Hazard was the architect of both, his searching cross from the right following a short corner finding the head of Loftus-Cheek, who headed home his ninth goal of the season. Three minutes later, Hazard's corner found the unmarked Luiz, who powered another header past Foster.
Pedro and Higuain both drew smart stops from the Watford goalkeeper before the Argentine finished the game with 15 minutes left, running onto Pedro's sharp through-pass before chipping the onrushing Foster from a tight angle.
With speculation linking him with a summer departure, this could have been Hazard's final Premier League game for Chelsea at Stamford Bridge.
If that is the case then it was a fine way to bow out, though it also gave Chelsea a sharp reminder of what they will be missing if the Belgian leaves.
Gary Cahill was brought on in the final stages for his first competitive appearance since November before his expected departure from the club at the end of the season.
Watford's hopes of finishing seventh were already over going into this game after Wolves' win against Fulham on Saturday, meaning they have to beat Manchester City in the FA Cup final if they want to qualify for the Europa League.
Watford head coach Javi Gracia named a strong side, including a return for captain and top scorer Troy Deeney after completing a three-match ban.
The Hornets boss says his players cannot afford to lose focus in their remaining league games with cup final starting places up for grabs. That was demonstrated by a lively start, with Deulofeu fizzing a 20-yard-effort just wide of the post before Deeney's powerful header was superbly clawed onto the post by Chelsea goalkeeper Kepa Arrizabalaga.
Jose Holebas then fired over the bar from just inside the area as Watford continued to dominate the opening stages, sparking murmurs of frustration from the home crowd.
But after working so hard in the opening 45 minutes, Gracia must have been frustrated at their slow start to the second period, conceding twice from set pieces in quick succession.
Deulofeu, the hero of Watford's FA Cup semi-final win over Wolves last month, continued to be a threat and was unlucky to see his low drive go just wide of the post with Kepa unmoved. Holebas then clipped the bar after stealing the ball from Mateo Kovacic just outside the area.
Watford's day was perhaps summed up when a late header from Isaac Success was ruled out after the ball inadvertently hit team-mate Andre Gray, who was in an offside position.
As well as scoring the opening goal, the England international made an impact all over the pitch, with no player making more tackles or interceptions
Chelsea boss Maurizio Sarri, speaking to BBC Match of the Day: "At the beginning we were tired physically and mentally. Then in the second half they lowered the intensity and we got in control of the match. It was very difficult in the first half and we were lucky because we scored two goals in three minutes and then after the second goal we were able to play good football.
"Ruben Loftus-Cheek is not just for me but for English football. He is improving match by match he can become one of the best midfielders in Europe, not only in England. He has very great potential and in the next season he will be for sure one of the best midfielders, not only in England.
"I don't know about Gonzalo Higuain's future, you have to ask the club. But for a striker it is not easy to play here, when you're used to playing in Spain and Italy. It's not easy to adapt to this competition because it's different physically. If he's staying then we can do very well in the next season.
"Gary Cahill is very important in the dressing room, very professional, he played only five or six matches this season but in training he was really very important for us. It was right to put him on the pitch for the last minutes."
Watford boss Javi Gracia, speaking to BBC Match of the Day: "It's difficult to accept this result because we had a good performance in the first half and had very clear chances to score but didn't take them.
"Then in the second half, they scored from a corner kick, the second from another corner. It was difficult for us but if you analyse the play of the team we did many things well. We didn't confirm in the first half when we played better and after that we didn't deserve this result.
"I'm sad because we knew at the first corner they will do this and they did it and they scored. We need to be more aggressive to defend, more aggressive to finish and more clinical. Only playing well is not enough to win in these stadiums.
"We need to improve, it's not just bad luck, we need to be more aggressive to finish the chances we are creating. We dominated possession; we played more in the opposition half. I like how we played but we need to be more aggressive in both boxes."
Chelsea welcome Eintracht Frankfurt to Stamford Bridge on Thursday for the second leg of their Europa League semi-final (20:00 BST). The Blues then travel to Leicester while Watford host West Ham on the final day of the Premier League season next Sunday (both 15:00).