At the break it looked as if this one could go either way, but Quins proved just too strong for Cardiff in the second half.
As well as the win, the Premiership champions got a try-scoring bonus-point in the bag and now sit top of Pool B - albeit with most other teams having just played one match.
A tight game in the opening 55 minutes but it was all too much for Cardiff after a challenging few weeks.
Marcus Smith and Dan Fish showed off in the first half with the game going into the sheds at 17 all before Marcus Smith Alex Dombrandt and Harlequins turned up the heat and secured a bonus point win.
Alex Dombrandt scored two tries for the Premiership champions, while Danny Care, Joe Marchant and Andre Esterhuizen each had one apiece.
