Daniel Ayala’s header and George Friend’s brilliant strike put Boro in control by half-time and Traore sealed their win with five minutes remaining.
They went ahead when Ben Gibson flicked on Grant Leadbitter’s 24th-minute corner and Ayala nodded home unchallenged at the far post.
Friend doubled the visitors’ lead 11 minutes later, smashing a left-footed shot from 25 yards beyond keeper Alex Smithies and into the top corner of the net.
It prompted Ian Holloway to send centre-back Joel Lynch up front until half-time, when the QPR boss made a double substitution, bringing on target man Matt Smith and winger Bright Osayi-Samuel.
But Middlesbrough, in their fifth match under manager Tony Pulis, rarely looked troubled.
And Traore made sure of the points by slotting past Smithies after being put through by Rudy Gestede.
“In the first 15 minutes we looked a little bit out of sorts and QPR started really brightly,” said Pulis.
“As soon as we got a goal we then went on and deservedly won the game. For the players to put in that kind of performance and show that bit of character, I’m really pleased.
“We played some good stuff at times, created opportunities, and when we had to roll our sleeves up and battle we restricted them to not many opportunities.”
Boro are the only side in the Sky Bet Championship yet to drop points from a winning position this season - and they never looked like doing so once in control against the R’s.
Early on, QPR’s Jack Robinson and Traore fired wide during a cagey start to the game.
However, once they went in front the visitors were largely comfortable.
Conor Washington did have a decent chance to pull a goal back shortly before the interval but shot straight at keeper Darren Randolph after being found by Robinson’s long ball.
Early in the second half, Rangers captain Nedum Onuoha sliced a shot high and wide of the target.
Massimo Luongo went closer with a right-footed half-volley and Smith header over from Luke Freeman’s left-wing corner, but Holloway’s team struggled to create clear-cut chances.
Boro would have added a third goal with 13 minutes remaining but for Robinson’s goal-line clearance.
Gestede, on as a substitute, shot past Smithies after being set up by Jonny Howson, but Robinson was on hand to deny the striker what would have been his first league goal since August.
Both keepers produced late stops shortly before Traore’s cool finish.
Randolph was down quickly to deny Lynch at close range before Smithies dived to his left to keep out a header from the lively Gestede, whose clever assist led to the third goal.
It was only the third goal of Spanish winger Traore’s senior career - and his first in the league.
QPR: Smithies, Onuoha, Lynch, Robinson, Furlong, Luongo, Scowen (Eze 70), Freeman, Bidwell (Samuel 46), Oteh (Smith 46), Washington. Subs Not Used: Ingram, Manning, Baptiste, Wszolek.
Middlesbrough: Randolph, Shotton, Ayala, Gibson, Friend, Howson, Leadbitter, Traore, Downing (Christie 87), Bamford (Clayton 72), Assombalonga (Gestede 69). Subs Not Used: Konstantopoulos, Braithwaite, Fletcher, Johnson.
Referee: Oliver Langford (W Midlands).