Chelsea later effectively ended Liverpool’s hopes of qualifying for the Champions League after the newly-crowned Premier League champions held them to a 1-1 draw at Stamford Bridge.
With two games remaining, fifth-placed Liverpool have 62 points from 36 matches, six behind Manchester United who occupy the final Champions League qualifying spot and have a better goal difference (+25 to +11).
Chelsea have 84 points from their 36 games, 11 more than second-placed Manchester City, who confirmed their place in next season’s Champions League.
QPR needed to win their remaining three fixtures to stand any chance of survival but a sorry defeat at the Etihad Stadium left them nine points adrift of 17th-placed Newcastle United.
“I don’t think it’s time for any post-mortems because our fate is now what it is,” QPR’s interim manager Chris Ramsey told Sky Sports.
“Everybody is very disappointed we’ve lost our status in the Premier League. We need to make sure we rebuild and give the fans and the people from west London another Premier League club in the next couple of years.”
It was almost three years to the day since Aguero’s dramatic goal deep into stoppage-time lifted City to a 3-2 win over QPR which secured their first Premier League title.
Rangers survived that day, only to go down the following season, and they arrived in Manchester this time knowing only victory would prevent them from joining Burnley in an immediate return to the Championship.
QPR have collected only seven away points this season and made the worst possible start when Aguero danced through the visitors’ feeble defence before chipping the ball over onrushing goalkeeper Robert Green.
In a rare foray forward, QPR’s Charlie Austin had a header ruled out for offside before Aleksandar Kolarov’s low free kick flew through the porous defensive wall and settled in the bottom corner.
Aguero added his second when he capitalised on Yun Suk-young’s error to race away and slot past Green and he completed his hat-trick from the penalty spot after Matt Phillips had felled David Silva.
James Milner added a fifth with a simple finish and Silva rounded Green to slot home after a sublime move to complete a miserable day for QPR.
GUARD OF HONOUR
Liverpool welcomed the champions with a guard of honour at Stamford Bridge but the hosts were in no mood to thank them as Chelsea’s Cesc Fabregas left his mark on Raheem Sterling with a heavy challenge in the opening minute.
Chelsea could have been forgiven for showing signs of a title hangover but they looked sharp early on and took the lead after five minutes when captain John Terry rose above Rickie Lambert to power a header home from a corner.
But Liverpool had their own captain to thank just before halftime as some slack Chelsea defending from Adam Lallana’s free kick allowed Steven Gerrard to sneak in at the far past and level the scores.
Chelsea goalkeeper Thibaut Courtois had to be alert to deny Sterling’s deflected cross in the second half before Jordan Henderson dragged a volley just wide as Liverpool made one final push to keep their Champions League qualification hopes alive.
“I think now this team’s got to prepare for next year. We wanted to make a statement with our performance today,” Gerrard, who is leaving for Los Angeles Galaxy at the end of the season, told Sky Sports.
“Unfortunately we didn’t win the game but we’ve shown that with a few additions we can compete next year.”
Fourth spot would guarantee United a Champions League playoff with the top three automatically qualifying.
Third-placed Arsenal are two points above United with two games in hand, including Monday’s visit of Swansea City.
(Additional reporting by Michael Hann; Editing by Ed Osmond/Mark Meadows)