Gary Deegan's tenth-minute strike proved to be enough for Coventry City against the R's in a lacklustre affair at The Ricoh Arena.
Deegan's fortuitous deflected strike won it for the hosts, after his effort came off the leg of a Rangers defender and nestled in the bottom right-hand corner.
Mick Harford would have been more than happy with the efforts of his side, but ultimately their failure to convert their possession into chances proved costly.
R's boss Harford made three changes to the side that was beaten at home in midweek by Ipswich Town.
Marcus Bent missed the trip to the Midlands with a hamstring injury, while Nigel Quashie and Hogan Ephraim also both made way.
That meant Peter Ramage, Akos Buzsaky and Tamas Priskin all came back into the side to face the Sky Blues.
On a bitterly cold afternoon at The Ricoh Arena, the R's forced a flurry of corners in the opening five minutes.
After Priskin won the first of three QPR corners, Cook's delightful centre almost completely deceived City keeper Keiren Westwood, who did well to just tip the ball over his own bar.
Moments later, another corner - this time from Buzsaky on the left - possessed just as much quality as Cook's, deceiving everyone but Connolly at the back post, who scuffed wide from close range.
Both sides were struggling to get the ball down on what was an atrocious playing surface.
However, on ten minutes, the Sky Blues' first shot on target saw them collect the opening goal of the affair.
After a long ball was played up to the Clinton Morrison, the former Crystal Palace striker touched the ball back into the path of Gary Deegan who, with the aid of a deflection, stroked the ball into the net past the helpless Ikeme.
Soon after, Rangers went on the attack down the right, and after Buzsaky cut in to fire over a cross-come-shot, his effort was comfortably collected by Westwood.
The Magical Magyar went even closer moments later.
After the lively Faurlin was tripped on the edge of the box, Buzsaky stepped up to curl a shot just wide of the left-hand post for Rangers.
Despite chances being few and far between, it was the Hoops who continued to pose the greater attacking threat, with the lively Cook and Faurlin at the heart of their positive play before the interval.
As the second half got underway, the R's and their counterparts City again struggled to get a hold of the game in this increasingly tight encounter.
Rangers had the first shot on target in the half, however, and when Cook won a free-kick from 25-yards out, he fired the resultant set-piece straight at Westwood in the Sky Blues goal.
Moments later, Connolly won possession on midway before releasing the ball to substitute Adel Taarabt, who could only drag his shot from the edge of the penalty area just wide.
The R's, by now, were enjoying more possession, as they went in search of a much-needed equaliser - and they almost got it.
Cook's teasing ball from the right into the box was diverted goalwards by City defender Leon Barnett, and keeper Westwood somehow managed to dive to his left to tip the ball away for a corner.
Soon after, Sky Blues right-back Stephen Wright attempted a speculative lob over Ikeme when he struck the ball towards the net from fully 40 yards from goal, but the Rangers keeper got back in time to claim the shot.
The R's enjoyed a greater amount of possession in the closing stages, though a Cook free-kick that sailed wide 25 yards from goal, and substitute Antonio German's low strike that flashed across the six-yard box, was all that they could muster.
Coventry City: Westwood, Wright, Clingan, Eastwood, Morrison (Sears 67), Deegan, Cranie, Baker, McIndoe, Barnett, Wood.
Subs not used: Konstantopoulos, Hussey, Walker, Grandison, Jeffers.
Goals: Deegan (10)
Bookings: Wright (41), Cranie (71)
QPR: Ikeme, Ramage, Stewart, Buzsaky (Taarabt 67), Gorkss, Connolly, Cook, Faurlin, Hill, Simpson, Priskin (German 55).
Subs not used: Cerny, Vine, Quashie, Balanta, Borrowdale.
Bookings: Connolly (66), Faurlin (70), Gorkss (75)
Referee: Mr D Foster
Attendance: 15, 247 (586)
