The home side took the lead after seven minutes through a penalty goal from fly-half Nick Evans.
Evans increased his side's advantage four minutes later with another penalty goal as Harlequins dominated the opening stages.
The visitors offered little and went down further to another penalty goal from Evans on 24 minutes. Harlequins ended a dominant first half with a try from Charlie Walker on 40 minutes.
Ben Botica continued on from Harlequins' first-half display with a penalty goal on 51 minutes. Racing fly-half opened up the away side's scoring on 59 minutes with a penalty goal to make it 17-3, and that is how the contest finished.