The undoubted highlight of a lacklustre encounter came from former England captain Lawrence Dallaglio who did a fine impersonation of Jonny Wilkinson by nailing a 25-metre drop goal after half an hour, before being forced off with a rib injury.
Wasps dominated territory in the first half but Leeds were kept in touch through the boot of Scotland fly-off Gordon Ross.
Leeds started at a ferocious pace, tearing into Wasps at the breakdown and harrying Matt Dawson around the base of the rucks and mauls.
Ross opened the scoring after three minutes when Wasps were caught offside in the midfield.
Wasps fly-half Alex King levelled the scores at 3-3 after 12 minutes.
Ross missed a penalty attempt a minute later and Wasps made Leeds pay on 15 minutes when Tom Voyce made a searing break down the left-hand touchline.
Prop Will Green showed tremendous pace in support and took the inside pass from Voyce to go over for the try. King converted from the left of the posts.
Ross struck his second penalty to make the score 10-6 to Wasps five minutes later.
Leeds scrum-half Alan Dickens was sin-binned on 24 minutes for an infringement at the breakdown.
Dallaglio proceeded to punish 14-man Leeds with his outrageous drop goal shortly after. There are many ways to silence a Leeds crowd and this was certainly one of them.
It was to be Dallaglio's last act as he went off three minutes later with a rib injury.
Ross kept Leeds in touch with his third penalty of the night and the sides turned round with the score 13-9 to Wasps.
The second half started scrappily with Leeds squandering several try-scoring opportunities through sloppy handling in the back line, Ross and Phil Christophers being the main culprits.
Phil Greening's disappointing return to first-team action ended on 60 minutes when he was replaced by Ben Gotting, Wasps' line-out having failed to function all night.
Wasps centre Peter Richards made a series of sniping breaks in yet another impressive display from the converted scrum-half.
The young Wasps player looks to the manor born in his new position and England centre Fraser Waters could struggle to reclaim his position when he returns from injury in the next couple of weeks.
Ross missed his third kick of the night on 71 minutes, going narrowly wide from the halfway line.
Leeds pressed frantically in the final 10 minutes but their lack of precision in their passing continued to cost them point-scoring opportunities.
Wasps' much-vaunted defence held firm with young Irish openside Jonny O'Connor putting in a series of fine tackles.
For Leeds Tykes:Pens: Ross 3
For London Wasps:Try: GreenCon: KingPen: KingDG: Dallaglio