The Royals had Yann Kermorgant sent off in the 81st minute for a second bookable offence, and needed their goalkeeper Vito Mannone to keep out a late penalty from Jake Bidwell to secure all three points.
The result has moved Reading above Bolton Wanderers into 19th position in the Championship table, while QPR stay in 15th.
The Royals were not to be denied four minutes later, however, with Aluko embarking on a solo run before finding the top corner of the net with a wonderful strike.
QPR almost levelled moments later when Conor Washington found space in a central position, but the forward fired wide.
The visitors did have the ball in the back of the net in the 41st minute when Joel Lynch flicked the ball past Reading goalkeeper Mannone, but the offside flag was raised.
QPR's first opportunity of the second period arrived in the 56th minute when Josh Scowen lined up a free kick outside the box, but the midfielder's effort was over the crossbar.
Mannone then made a stunning save to deny Paul Smyth in the 67th minute as the pressure from the away side continued.
QPR's challenge was boosted in the 81st minute when Kermorgant picked up a second yellow card for a late challenge on Darnell Furlong, which left Reading with 10 men for the final stages.
The away side had a golden chance to level the scores in the 92nd minute when Pawel Wszolek went down inside the Reading box, but Mannone kept out Bidwell's penalty as Reading secured all the points.
READING (4-2-3-1): Mannone; Gunter, Ilori, Moore, Blackett; Edwards, Van der Berg (Bacuna 55'); Barrow, Swift, Aluko; Martin (Kermorgant 62')
QUEENS PARK RANGERS (4-2-3-1): Smithies; Furlong, Onuoha, Lynch, Bidwell; Cousins (Luongo 74'), Scowen; Wszolek, Freeman, Smyth (Eze 74'); Washington (Smith 58')