The home side - playing in front of a season-best crowd of 10,014 - secured the win when Samoan flyer Lemi beat replacement scrum-half Nicolas Vergallo to Joe Simpson's grubber to score a try.
Shaun Edwards said Wasps had no issues with dropping down to the Amlin, insisting the competition was growing in stature.
"If we manage to get past Harlequins then we would go on to face either Brive or Munster," said the head coach. "It's going to be something of a rugby jamboree in a pretty good party town, so hopefully, we'll be there."
Meanwhile, Australia hooker Huia Edmonds, 29, said today he will join Saracens this summer from Canberra-based Brumbies.