Former Leicester and England flyer Tom Varndell, on the opposite wing, also touched down for the home side.
Their other 17 points came from the boot of Welsh fly-half Nicky Robinson, who landed five penalties and a conversion on his return from a three-match injury-enforced absence.
Bath replied with tries from 20-year-old prop Kane Palma-Newport and flanker Guy Mercer with 19-year-old fly-half Tom Heathcote marking his first senior start with a 14-point kicking haul.
Heathcote kicked Bath into a first-minute lead with his opening penalty but Robinson replied with two for Wasps to edge them 6-3 ahead after 12 minutes.
The hosts stretched their early lead to 13-3 when full-back Hugo Southwell's through-kick was deflected into the hands of winger Wade, who grabbed the opportunity to race in from 25 metres.
Lively scrum-half Michael Claasens was the springboard for most of Bath's early attacks.
His quickly-taken tap penalty put the home side on the back foot and another attack instigated by the South African's break ended with prop Palma-Newport driving over from close range.
Bath crossed the line twice more midway through the first half but were denied tries on both occasions.
Full-back Nick Abendanon's break split the home defence and he found Heathcote on the inside but the young fly-half was held up over the line by the combined efforts of Wasps scrum-half Nic Berry and flanker Joe Launchbury.
A minute later centre Ben Williams dived over but referee Andrew Small judged that he had lost control of the ball as he stretched to touch down.
Bath suffered another blow when they lost hooker Pieter Dixon, replaced by Ross Batty, in the 29th minute.
But Heathcote kicked them level with his second penalty on the half-hour mark.
It took Wasps only three minutes to go ahead again with a superbly-crafted try finished by Varndell.
Launchbury and Robinson moved the ball quickly to send speed merchant Varndell sprinting in down the left wing for his second try of the season but Robinson suffered his first kicking miss from four attempts as the difficult touchline conversion went wide.
Bath squandered a clear chance to draw level when a width-of-the-pitch passing movement ended with Abendanon failing to find unmarked right-wing Matt Carraro with the final pass.
Heathcote and Robinson exchanged further penalties at the start of the second half as Wasps maintained their five-point lead before Heathcote missed the chance to narrow the gap once more when his 45-metre penalty kick into a stiff wind fell short.
The Bath youngster made amends in the 58th minute, landing his fifth kick from six attempts to cut the gap to two points.
But Robinson again matched him, responding with his fifth out of six three minutes later before narrowly missing with a drop goal attempt from the halfway line.
Bath, conceding a rash of penalties, were punished again when Robinson landed his sixth kick with a 65th-minute penalty.
A sustained late spell of Bath forward pressure produced a 73rd-minute try for Mercer which earned them a losing bonus point - the least they deserved for their efforts.
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