Elia ushered in an anxious final half-hour after he was sent off by referee Luke Pearce for a dangerous tackle on Dan Robson that tipped the Wasps scrum-half past the horizontal.
Until that point Quins had been in full control, reflected by a 20-8 lead built on two tries by Alex Dombrandt and one more from Marcus Smith, but which owed everything to Robshaw’s feverish work at the breakdown.
Elia’s dismissal shifted the balance instantly, however, and the contest became a question of whether Wasps could overhaul the deficit in the 27 minutes available.