Irish had won three Premiership games in succession for the first time since 2011 and looked set for a fourth when they led 14-10 at half-time.
But Wasps finished strongly to claim a bonus point win.
Irish took a sixth-minute lead with a solo try from Meehan. From a ruck 15 metres out, the scrum-half chipped into a gap between two defenders before regaining possession to dart over.
Myler converted before Wasps responded with a straightforward penalty from Gopperth.
Irish should have extended their lead when Loader hared through an opening in the visitors' defence but the flying wing lost possession when he was tackled by Paolo Odigwu close to the line.
A storming 50-metre run from Australian international lock, Adam Coleman, secured Irish a platform in the opposition 22. From there, they scored the try their dominance deserved when Loader outflanked Wasps' cover to score.
However the loss of Rowlands seem to spur on the visitors to dominate the last seven minutes of the half and they were rewarded when Alo forced his way over from close range. Gopperth's conversion left Wasps trailing 14-10 at the interval.
Six minutes after the restart, Wasps took the lead for the first time. Jack Willis won a crucial turn-over in his own half before Robson darted away from a line-out with a kick and chase. The ball eluded the scrum-half but Harris was up in support to scramble his way over with the try being awarded after countless TMO replays.
The game was slipping away from the hosts so four substitutions were made in one hit and it paid immediate dividends as one of them, Sekope Kepu, made ground from a driving line-out to set up a try for Rogerson.
Myler missed the touchline conversion so the game was firmly in the balance as Irish led 19-17 going into the final quarter.
But Wasps continued to be much the better side in the second half and regained the lead when a neat round of passing culminated in Watson crossing. Then late tries from Robson and Umaga sealed victory.
It was game over for Irish but they showed tremendous resolve in the dying stages to earn a bonus point when Matu'u finished off a driving line-out.