Torres, who famously suffered a 24-game goal drought this season, picked up where he left off against Barcelona with a bustling performance and three well-taken finishes.
Daniel Sturridge had opened the scoring with a long-range effort after just 46 seconds, with John Terry adding a second with a header as he responded to his sending off in the Champions League win at the Nou Camp with a good performance.
Substitute Florent Malouda added a sixth with 11 minutes remaining, with Djibril Cisse threading a late consolation past Petr Cech to give him the unusual statistic of having scored or been sent off in every match he has played for QPR.
The result means Chelsea stay sixth, but are just one point behind Tottenham and Newcastle in fourth and fifth respectively.
QPR, meanwhile, sit above third-bottom Bolton Wanderers on goal difference, although the Trotters have a game in hand meaning the Hoops face a monumental battle to stay up with two matches remaining.
Chelsea were in fine form but their local rivals QPR were dreadful, quite literally from kick-off: In the first attack of the match, Sturridge was given a second bite of the cherry after Anton Ferdinand’s block before, from the left edge of the box, flashing an excellent effort into the top left corner.
Frank Lampard was arguably standing in an offside position when Sturridge shot but, whether blocking Kenny’s line of sight or not, the QPR goalkeeper was culpable for letting the ball in at his near post.
Kenny did better 12 minutes later, readjusting well to tip Lampard’s chip over, but he failed to keep out Terry’s angled header at the resultant corner. Though not at fault per se, Clint Hill was too easily beaten to the header by the England defender.
Two goals down and missing suspended playmaker Adel Taarabt, the visitors were struggling to string two passes together. Chelsea, meanwhile, were finding things all too easy - as one may expect from a team that just knocked Barcelona out of the Champions League.
And on 19 minutes they effectively ended the match as a contest when Salomon Kalou, whose place is under threat following the signing of Germany winger Marko Marin, fed Torres, who rounded Kenny to slide the ball into the net, a not dissimilar finish to that which dumped Barca out of Europe on Tuesday.
What followed was disastrous, even by QPR’s standards: right-back Nedum Onuoha initially made the correct decision to allow a head-height ball to go back to the advancing Kenny, but he inexplicably changed his mind mid-second, heading the ball away from his keeper’s grasp, the pair colliding as Torres smashed the finish home.
It was worse than farcical and, with Chelsea four goals up, they chased a cricket score with the goal difference likely to come into play in the race for Champions League places.
Kenny denied Lampard, Sturridge was kept at bay by Hill and Torres fired just wide, with QPR captain Joey Barton lucky to escape a card after he caught Juan Mata late on the ankle.
The second half started slowly as Chelsea sat back, Mata guilty of a glaring miss on the break as he shot weakly at Kenny after Kalou sent him clean through.
Jamie Mackie had a rare effort for the visitors, his long-range effort deflected off Terry and well-saved by Cech, but it was business as usual soon afterwards as Kenny was forced to deny Torres.
On 64 minutes QPR spurned a good opportunity when Mackie failed to pick out the unmarked Cisse: Chelsea countered and Mata slipped a low pass through to Torres, whose diagonal run sent him clear in the left channel, and whose low finish flew across Kenny and inside the far post for his hat-trick.
It was 5-0 but that was still not enough, as Sturridge saw a drive deflected inches wide, while Malouda fired just off target and substitute Ramires - who scored against Barcelona but will miss the Champions league final through suspension - forced a good save from Kenny.
The Brazilian should have passed then and he elected to do so a minute later, finding Malouda after a surging run down the line, the Frenchman making no mistake from close range.
Cisse pulled one back for Mark Hughes’s side, drilling a low finish across Cech after a good run and cross from Onuoha, but it was a personal boost and nothing more as QPR were well beaten.