But Northampton's first away win in the league this season takes them above Wasps into sixth in the Premiership table.
The game's early stages had few chances but Saints' in-form Russian Vasily Artemyev was barged into touch by Christian Wade after a charging run.
Wasps had to play 10 minutes with 14 men early on when Tim Payne was sin-binned for squaring up with Jon Clarke and swinging a punch.
And the Saints took the lead in his absence, with Lamb scoring a simple penalty. But that only lasted three minutes and Wasps scored the first-half's sole try, when Northampton's Chris Ashton lost possession on the floor under pressure from Tom Varndell and a speculative pass from Wade over his own head found Flutey in the corner to touch down, although Nicky Robinson missed the conversion.
Lamb and Robinson swapped penalties and the Saints fly-half failed with an effort, which appeared to fly over the post but the fourth official decided not to award the three points.
But Lamb did put the Saints in control with two more penalties, although he kicked another one just wide on half-time as they led by four points.
And three minutes after the break, they scored their first try, with Tonga'uiha picking the ball up from close range and crashing over for his first try in over a year. His last touchdown, the second of a brace, was in
the corresponding fixture last season.
But Wasps were livid as Lawes had played a forward pass to the lively Artemyev in the build-up.
Lamb missed the conversion and then a penalty in a mixed day in front of the posts.
But Mujati made Lamb's missed kicks largely irrelevant when he powered his way under the posts after charging through, and the Saints fly-half kicked the easiest of conversions.
Wasps looked set to claw themselves back into the game after a great kick by Joe Simpson but Artemyev's pressure denied Wade the chance to collect the ball and touch down.
But they did get their second try when Ross Filipo pounced over the line. Robinson missed the conversion and despite pushing for another there was no way back into the game.
Wasps director of rugby Dai Young:
"Take it back two or three steps before that and we got turned over twice which gave them that opportunity to be there [for Saints' first try].
"I'm a big believer that you can only control what you can control and we have got to look at ourselves.
"It's no good looking for excuses elsewhere. You have to find a way to win and we didn't do that.
"The biggest grievance to us was the tackle area - how that was refereed or not refereed.
"Refereeing's not an easy job, otherwise everybody would be doing it. It's not fair to stand here and criticise. There's proper channels to do it and we're going to have to look at it if we feel there were mistakes made."
Northampton rugby director Jim Mallinder:
"We weren't brilliant today. We did enough to win but we'll probably need to do a little bit more if we're going to beat Munster next weekend.
"We conceded a sloppy try but generally our defence was quite good. But defensively, we gave away a few too many penalties.
"You've got to listen to the referee - and Mr Wigglesworth does things slightly differently - so you've got to work with him.
"We've now got on a bit of a roll and we're keen on keeping that momentum going."
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