The former Tottenham Hotspur winger scored his first goal for the club to earn all three points, despite Eduardo Vargas cancelling out Seamus Coleman's first-half openerAaron Lennon scored his first Everton goal as they rebounded from their Europa League disappointment to inflict another blow to QPR's Premier League survival hopes with a 2-1 win at Loftus Road.
A 5-2 defeat at Dynamo Kiev on Thursday saw Everton crash out 6-4 on aggregate at the last-16 stage, ensuring there will be no English representation in the Champions League or Europa League last eight.
However, Seamus Coleman's excellent driven effort put the visitors back on the winning trail and ahead by half-time on Sunday.
Substitute Eduardo Vargas lashed home a close-range equaliser in the 65th minute as struggling QPR looked to claim a crucial point, but Lennon placed home the winner with 13 minutes left to break the hosts' valiant resistance.
QPR will perhaps feel disappointed not to take something from the game after they competed well throughout, Junior Hoilett and substitute Adel Taarabt both rattling the crossbar in the second half.
But Everton, heavily criticised for their defensive showing in Kiev, looked far more assured at the back to see out a result that means Chris Ramsey's QPR remain four points adrift of safety with just eight matches remaining.
Everton headed to London just six points above the drop zone themselves, but their second consecutive league win leaves them 13th and has now eased any lingering relegation fears.
QPR enjoyed the better of the early exchanges, with Bobby Zamora - one of four changes from the 3-1 defeat at Crystal Palace - causing problems with his physicality.
They failed to create clear-cut chances, though, and Everton took the lead with a fine team goal in the 18th minute.
Lennon laid Arouna Kone's cross from the left in to the path of Leon Osman and he rolled the ball out to Coleman, who hit a sweet first-time effort high into the left-hand corner.
Everton felt they should have had the chance to double their lead from the penalty spot when Joey Barton, back in QPR's XI after a three-match ban, appeared to block Darron Gibson's drive in the penalty area with his hand.
QPR remained a threat going forward and Zamora wasted a great opportunity when he failed to make clean contact with a header from Charlie Austin's fizzed cross.
They went even closer a minute after the break when Hoilett's fierce 25-yard effort crashed off the woodwork. Matt Phillips' header towards goal from the rebound caused confusion, but the winger was ruled offside before Zamora bundled in the loose ball.
Ramsey looked to change things by introducing Vargas for Hoilett on the hour, and the move paid dividends five minutes later.
Sandro and Austin caused panic in the Everton penalty area and Vargas pounced to lash home from inside the six-yard box for his second league goal of the campaign.
Parity lasted just 12 minutes, though, as Nedum Onuoha nipped in front of Kone to block Coleman's cross, only for the ball to fall kindly for Lennon and the winger coolly converted into the bottom left-hand corner.
QPR threw caution to the wind by bringing on the enigmatic Taarabt for the closing stages, and the Moroccan twice went agonisingly close to rescuing a point - first curling a shot narrowly wide of the right-hand post, before striking the crossbar in injury time.