Two first half goals seal visiting win.Grego-Cox could have completed his hat-trick late on but drove over the bar and it was just the two goals in the end in an entertaining game.
The U's were still creating plenty of chances though and first Sembie-Ferris drove just wide, before Bonne was twice denied after escaping the offside trap in the final quarter of the match.
Vincent-Young moved inside to centre half as a result of the substitution and he was in the right place to quickly block two R's efforts as the visitors sought a decisive third.
On the hour mark, Olufemi came on for his second game since recovering from injury, replacing Harney.
Not long after half time, Lewington pulled off a great reaction save as the ball eluded Harney from a left sided cross.
The U's made two changes at the start of the second half, as Curtis and Marriott came on for Moncur and Healey.
A free kick on the edge of the box struck the wall and was there to be won and it was Grego-Cox who was on the mark to slot home despite calls for offside.
The R's doubled their advantage just before half time.
The U's sought a path back into the game, with Moncur and McEvoy both denied, and it was an end to end match as the rain started to fall.
But four minutes later, the R's were ahead as Grego-Cox bent one home from the edge of the box that beat Lewington as it found the bottom corner.
Shortly afterwards, Lewington pulled off a fine stop with his feet from the marauding Gibbons.
The U's pressing game was causing problems for the visiting defence in the early stages and the home team had three chances in quick succesion before Grego-Cox escaped at the other end for Rangers before pulling his shot just wide.
And they went close early on as the tenacious Healey had a shot that looked destined for goal until it hit Macauley Bonne on its way towards the goalline.
Colchester named a strong side, with Chris Lewington, George Moncur and Rhys Healey all starting.
The game was one full of decent chances, but it was QPR who found a path to goal on a wet and windy afternoon at Florence Park.
Two first half goals were enough to bring the U's unbeaten start to 2015 to an end on Thursday afternoon.