The R’s needed a win to stand a chance of staying up, but were behind after just four minutes as Aguero finished from eight yards.
Aleksandar Kolarov’s trademark free-kick put City two up after 32 minutes, before Aguero added a second from 15 yards and completed his hat-trick from the penalty spot after the break.
James Milner hit the fifth from close range and David Silva rounded off the win three minutes from time to confirm City’s top-four finish, as QPR taste relegation for the second time in three seasons.
Chris Ramsey’s side started the game on the back-foot, and were nearly behind through City’s first attack, Aguero seeing his effort from close-range blocked by Richard Dunne.
Aguero got his first a minute later, gliding past Clint Hill and getting a lucky bounce from Matt Phillips’ interception to dink the ball over Rob Green.
Milner misjudged an Aguero cross at the back-post with the goal gaping as City dominated the first half-hour, and they were rewarded with a second on 32 minutes.
After Richard Dunne had fouled Aguero 25 yards out, Kolarov curled his free-kick around the wall and past Green for his second set-piece goal in three games.
City nearly added a third minutes later as Green tipped a Silva effort wide from 12 yards, but QPR did hit the bar after Leroy Fer’s lobbed effort before half-time, one of the bottom-club’s rare bright moments.
Aguero grabbed his second after the break when QPR midfielder Yun Suk-young miscontrolled, slotting past Green when through one-on-one.
Frank Lampard missed a chance from six yards out moments later, before Green made two good saves to keep the score at 3-0, first from Silva’s low effort and then from Kolarov’s curling free-kick.
Aguero converted a penalty for his hat-trick on 65 minutes after Phillips had barged Silva, his 25th league goal of the season and fifth treble in a City shirt, before Milner converted the Argentine’s cross to make it 5-0 with 20 mintues remaining.
Substitute Wilfried Bony hit the post with a low effort from outside the area, but City got their sixth and final goal of the game through Silva, rounding Green to slot home from an angle after Bony’s fine backheel.
The defeat was QPR’s 14th away from home this season, and means City cannot mathematically be caught by Liverpool in the race for the top four spots.
Man City: Hart (6), Zabaleta (7), Demichelis (6), Mangala (6), Kolarov (7), Fernando (7), Milner (7), Fernandinho (7), Lampard (7), Silva (8), Aguero (9)
Subs: Toure (6), Navas (5), Bony (7)
QPR: Green (7), Yun (3), Caulker (4), Dunne (5), Hill (4), Phillips (4), Barton (4), Henry (4), Fer (4), Austin (4), Zamora (4)
Subs: Wright-Phillips (5), Kranjcar (5), Hoilett (5)
Man of the match: Sergio Aguero