Although Tottenham returned to fourth place with a 2-0 win over Blackburn, Fernando Torres' first hat trick in more than 2 1/2 years helped confirm that Chelsea is the in-form team of three aiming to qualify for Europe's club top competition.
Chelsea, which could yet render the race for fourth place immaterial if it wins next month's Champions League final, hit four goals in the opening 25 minutes at Stamford Bridge and only conceded with six minutes left.
The Blues reached the Champions League final in midweek by completing a two-legged win over Barcelona and would qualify as defending champion if it beats Bayern Munich for the trophy, leaving England's fourth-place team to enter the second-tier Europa League instead.
"After a Champions League game in midweek, it always proves difficult in the next game in the Premier League," Chelsea interim manager Roberto Di Matteo said: "I have to say that the team surprised me. I wasn't expecting but I was hoping.
"They really put in a great performance today."
Daniel Sturridge scored after 49 seconds, John Terry headed in a corner and the rejuvenated Torres scored twice to put the result beyond doubt with more than an hour remaining.
The Spain striker's first goal was very similar to the one that earned a 2-2 draw at Barcelona. He knocked the ball around the goalkeeper with one touch and rolled it into an unguarded net with his next.
He made it 4-0 after goalkeeper Paddy Kenny had dropped the slippery ball following a header back to him from teammate Nedum Onuoha.
Torres struck again in the 64th for his first hat trick since September 2009, when he scored three times in Liverpool's 6-1 win over Hull, and substitute Florent Malouda scored in the 80th.
Djibril Cisse got a late goal back for relegation-threatened QPR.
After just eight goals in his first 61 games since joining Chelsea for 50 million pounds ($81.3 million), Torres now has four from his last two matches.
"I was feeling very good, very sharp, playing well, but I couldn't score," Torres said. "Now I feel I'm not playing as well as before, but I am scoring goals, which is the important thing for the strikers."
With Chelsea fans looking forward to next month's Champions League final and FA Cup final, the opening half-hour was played in a party atmosphere despite heavy rain that meant water splashed with players' every footstep and the ball barely travelled when passed along the ground.
Still, a large number of Chelsea fans jeered and taunted QPR defender Anton Ferdinand throughout for his accusation earlier this season that Terry had racially abused him.
Terry lost the England captaincy and faces a criminal trial after the European Championship in the summer.
The furor meant that the traditional pre-match handshake between the sides was abandoned Sunday to avoid the players coming into contact outside of the game.
Defeat further damaged QPR's chances of avoiding relegation, although it is still just above the bottom three on goal difference.
"We've damaged our own goal difference today," QPR manager Mark Hughes said. "At halftime we talked about that."
Chelsea next hosts fifth-place Newcastle on Wednesday, when Tottenham is at Bolton.
Rafael van der Vaart and Kyle Walker scored Sunday for Tottenham, which had 19 shots to none by relegation-threatened Blackburn.
Van der Vaart put Spurs ahead in the 22nd after Gareth Bale's header from a cross by Aaron Lennon hit the bar, but the home side's comprehensive domination yielded only Walker's 75th-minute strike after that.
Tottenham's second win in 10 matches lifted it above Newcastle, which crashed 4-0 at Wigan on Saturday, on goal difference and to within four points of third-place Arsenal.
Chelsea is a point further back with three games remaining.
The title race resumes Monday, when defending champion Manchester United travels to second-place Manchester City — with just three points separating the sides.Suggest a correction