Young winger Christian Wade ran in a hat-trick to help Wasps come from behind to beat Leicester at Adams Park.
Visiting centre Billy Twelvetrees was responsible for all the Tigers' 29 points with two tries, which he converted himself, and five penalties, but still ended up on the losing side.
Nic Berry got Wasps' other try, while Nicky Robinson and Ryan Davies shared their other points with the boot.
Leicester have now started the new season with back-to-back defeats.
But Twelvetrees' individual contribution, completed with a late penalty, at least secured a losing bonus point.
Leicester, beaten at home by Exeter last weekend, continue to function under the handicap of being without 11 players on World Cup duty, and five out injured.
As for Wasps, having beaten reigning champions Saracens at Twickenham last weekend, even allowing for the current Premiership imbalance caused by events out in New Zealand, a second straight win made it a dream start for new rugby director Dai Young.
The hosts fielded five home debutants in Hugo Southwell, Chris Bell, Robinson, Marco Wentzel, Jonathan Poff and Robinson. But scrum-half Charlie Davies failed a fitness-test an hour before kick-off and was replaced by Berry.
The weakened Tigers made a lively start and were already 6-3 up from an exchange of early penalties when Twelvetrees finished a neat passing sequence by scoring on the right.
Christian Wade certainly has pace, and tries don't come much better than his second. I want England to pick him now, immediately, whisk him down to New Zealand - so we don't have to face him again
Leicester rugby director Richard Cockerill
But Wasps were rewarded for enterprising rugby on 27 minutes when Southwell broke out from deep, Wade's pace on the right left two would-be tacklers trailing, and his pass inside sent Berry scooting clear to score.
Wade then scored a fine try of his own on 35 minutes after Tigers old boy Tom Varndell had done the damage up the left.
Back stormed Leicester, fly-half George Ford setting up Twelvetrees to score by the posts. And Robinson thought he had levelled on the stroke of half-time, but his penalty from wide right struck the near post and bounced wide.
Twelvetrees continued his points-fest five minutes after the break with a penalty, but Wasps replied with one of the tries of the season so far.
There seemed no more than moderate danger when Southwell passed to Wade deep inside their own half. But the young wing twice shaped to pass only to accelerate into the Tigers half and swerve outside two challengers for a memorable score.
Robinson's conversion hit the post - his fourth failure from seven shots at goal - and he limped out of the game seconds later, replaced by Davis, who fired his team with his first penalty.
The ruthless Twelvetrees regained the lead for Leicester with a 64th-minute penalty after Wasps went offside in front of their posts.
But Davis kept the see-saw effect alive, scoring on 69 minutes, the fifth time the lead changed hands. And, when Wade darted behind two defenders to win a race for a box-kick from Berry, to complete a treble in only the former Wasps academy player's sixth first-team game, victory was secured.
POST-MATCH VERDICTS
Wasps rugby director Dai Young:
"Christian Wade is a rare commodity. Give him the ball and people shift to the edge of their seats in anticipation. Considering his age, that's very impressive. But he's very new to this level and we'll make sure he's brought along at a sensible pace.
"You have to be realistic. Nobody goes into a game thinking anything other than why you can win. But you do feel good about winning games likes the ones we've won.
"You can be over the moon, as long as you accept that both were also games we could have lost. I am aware of that and so are the squad. Last season's stats show that Wasps had the worst line-out and the worst scrum which is why they finished ninth. So we are a work in progress, working to improve."
Leicester rugby director Richard Cockerill:
"I'm pleased with the lads because there's losing and then there's losing after playing well.
"Had we been a bit smarter near the end, used line-outs to our advantage, we could have come away winners, but the lads put in a lot of good work.
"They tell me this is the first time we have lost the first two games of a Premiership season, so I guess I'm setting records of some kind. But, if we continue showing this work ethic the wins will come.
"We all know that Billy Twelvetrees is a quality player and he did ever so well to step up at the end and kick that goal to make sure we went home with at least a point. We deserved the point, but were punished for making too many errors."
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