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Varndell fed Wade to score a brilliant breakaway try in the early stages after Welsh failed to capitalise on a spell of persistent pressure.
Gavin Henson kept Welsh firmly in contention with a pair of perfectly-struck penalties.
The home side continued to pile on the pressure and were rewarded when Marco Wentzel found Wade before he returned the favour to pick out Varndell in space for a superb score.
Lee Thomas made no mistake with a drop goal from distance to put Wasps 16-6 ahead at the break.
Wade was it again early in the second half, cutting back inside Tom Voyce to extend Wasps' lead.
Varndell made the game safe 15 minutes from time with his sixth try of the year with a tight finish in the corner.