Wasps had burst into an early lead as soon as three minutes into the game when their new signing and former Bath wing Tom Voyce crossed the line for the opening try, converted by Mark van Gisbergen.
Quins grabbed three points back courtesy of a penalty by Irish fly-half Paul Burke three minutes later, although Van Gisbergen nudged Wasps ahead shortly after with his opening penalty of the match.
Burke dropped a goal for the hosts, before three quick-fire penalties for Van Gisbergen gave the champions some breathing space.
But they had not accounted for the searing pace of Harlequins' exciting England Sevens star Ugo Monye, with the young wide-man going over on the 40-minute mark for Quins' first five-pointer of the afternoon, Burke converting.
And the resurgence continued when new signing from Leinster, Andy Dunne touched down after 46 minutes, the extras again being struck by the reliable boot of Burke.
Wasps did not lie down however, and veteran wing Shane Roiser hit back with a try almost straightaway after Dunne's score, but it was to be the champions' last points of the day as Harlequins headed for the finish line in front of a sell-out Stoop crowd.
A 54th-minute penalty from Burke got them going, before Monye swooped for his second try with 10 minutes still left on the clock, the Under-21 star completing his brace as Burke added the extras in the last score of the match for his side.
Van Gisbergen secured a bonus point for his side in the last minute of the game with a penalty, in what will have been scant consolation to their coach Warren Gatland.
So, for Wasps, a losing start to their campaign in the absence of last year's captain Lawrence Dallaglio, but for Quins, a sign that better things may be around the corner after years of underachievement. However, it is early days only.
For NEC Harlequins:Tries: Monye 2, DunneCons: Burke 3Pens: Burke 3DG: Burke
For London Wasps:Tries: Voyce, RoiserCon: Van GisbergenPens: Van Gisbergen 5