The match was the first domestic fixture to be staged overseas and was played in perfect conditions in the luxurious grounds of the Emirates Palace Hotel.
Karl Dickson crossed twice for the victors, with further efforts by George Lowe, Ceri Jones and Sam Smith ensuring a bonus-point win. Tom Varndell and Joe Launchbury weighed in with the tries for Wasps.
The win sees Quins climb to the summit of Pool Four, ahead of Exeter and Bath, while Wasps stay second in Pool One with only one round of games remaining.
Gloucester moved to the top of Pool Three in the LV=Cup with a comfortable 30-16 bonus-point victory over Leeds Carnegie at Headingley.
Gloucester's defeat here on New Year's Day had given Leeds their only domestic win of the campaign to date, but there seemed little chance of a repeat as tries from Lesley Vainikolo and Tom Voyce plus a conversion and penalty from Freddie Burns gave the visitors a 15-9 lead, with Ceiron Thomas kicking three penalties for the hosts.
Burns further extended Gloucester's lead with another penalty and, despite a fine try for Leeds from Scott Mathie, Nick Wood and Tim Molenaar crossed to give the west-country side the extra point and leave them knowing a win over London Irish next weekend will put them into the semi-finals for the third year running.
London Irish collected their first LV= Cup win of the season by convincingly defeating the current holders Northampton 37-20 in an entertaining game at the Madejski Stadium.
Irish fielded a much stronger side than Saints, with the home line-up containing around half of their first-choice XV, and the selection paid dividends.
Even allowing for a very slow start, Irish were always the more powerful and penetrative side. Hooker Brian Blaney starred with his first two tries for the club before stint in the sin bin for deliberate offside. George Stowers, Steffon Armitage and Daniel Bowden also breached the Saints line.
Victory kept alive their remote hopes of qualification for the semi-finals, with Northampton's progress hinging on them defeating Leeds at Franklin's Gardens next week and hoping other results go in their favour.