The visitors outscored their hosts by four tries to one, with the boot of Exiles fly-half Mark Mapletoft keeping the home side in touch after Wasps had run into a useful 17-3 lead.
Lock Richard Birkett put Wasps on the scoreboard with a try in the second minute, which fly-half Alex King converted, before King slotted a penalty to stretch that lead to 10-0.
Left-wing Tom Voyce was next on the scoreboard for Wasps, with King again adding the conversion, before Mapletoft eventually put his side on the board on the stroke of half-time.
The self-same Mapletoft then began to chip away at Wasps' lead, as he struck two penalties and a drop-goal to take the score to 17-12 after 62 minutes. King, however, struck a penalty just two minutesl later to put his side ahead by more than seven points and when Mark van Gisbergen – who was playing at fullback – got over in the 74th minute it was officially game, set and match at 27-12.
But the scoring was not complete in the match as Exiles fullback finally got over for his team's first try – some three minutes from time – and Mapletoft added the conversion.
Wasps replacement back Ayoola Erinle had the final say in the match when he touched down in the 79th minute, King again added the conversion, and it was probably the most crucial score in the game as it confirmed their fourth – and bonus point clinching – try.
For London Irish:Try: HorakCon: MapletoftPens: Mapletoft 3DG: Mapletoft
For London Wasps:Tries: Birkett, Voyce, Van Gisbergen, ErinleCons: King 4Pens: King 2