A 10th defeat in 11 games leaves them just eight points above bottom club Newcastle, who lost to Worcester on Friday night, and their showdown at Wasps' ground in the final game of the season could decide who drops into the Championship.
Northampton's sixth win in their last eight games moved them into third place above Leicester, who meet London Irish on Sunday, and while they deserved to win on Saturday, they left it until the 75th minute to score the bonus point try.
That came from substitute scrum-half Martin Roberts, the others going to England full-back Ben Foden (2) and centre James Downey, with Ryan Lamb kicking two penalties and two conversions and replacement fly-half Stephen Myler a penalty.
Wasps' points all came from the boot of fly-half Nicky Robinson, who kicked five penalties.
Northampton were without hooker Dylan Hartley and flanker Calum Clark, who both face disciplinary hearings next week, but England winger Chris Ashton returned for his first game since January when he had a bust-up with director of rugby Jim Mallinder.
Wasps have had a shocking time with injuries and their curse struck again in the warm-up when replacement Ryan Davies picked up a knock and was replaced by teenager Tom Pridie, who is on loan from Ospreys.
Despite their problems, Wasps made all the running early on, had the edge in the scrum and, but for a forward pass, might have scored through full-back Hugo Southwell.
But their injury jinx struck twice more, centre Dominic Waldouck and flanker Jonathan Poff both going off, and they went in at half-time trailing 22-9 having shipped three tries.
Wasps led 9-7 after 23 minutes, thanks to three penalties from fly-half Robinson - who also missed one -
to a try by Foden, who latched onto a chip ahead by centre George Pisi.
Fly-half Ryan Lamb, who had missed a 13th minute penalty, missed the conversion and he was also wide with a relatively easy conversion of Saints' second try.
It came in the 28th minute when England scrum-half Lee Dickson put centre James Downey through a large hole straight from a scrum, while Waldouck was at the other end of the field receiving treatment.
Northampton began to take a stranglehold on the game after that and Lamb made it 15-9 with a penalty.
Saints could easily have conceded a try but Wasps winger Richard Haughton, back again after injury, failed to gather a loose ball just outside his own 22 and with a free run to the line.
To add insult to injury Poff left the field holding his nose as Lamb was lining up his kick. Although he
returned after half-time, he lasted only a minute and was replaced by John Hart.
Wasps, however, were at fault for Saints' third, which came after a knock-on by the visitors. Saints countered from their own 10-metre line and, after great work by Ashton and some fine inter-passing, Foden scored his second of the night.
Lamb's brilliant touchline conversion showed his radar was working again.
Robinson kicked his fourth penalty four minutes after the break and after the Saints prop Ben Broster and Wasps hooker Andy Long were sin-binned after a scuffle, Lamb missed a difficult penalty.
He made no mistake with a simple penalty in the 54th minute but that was cancelled out by Robinson five minutes later.
The second half was a fractious, error strewn affair and Wasps had Robinson sin-binned six minutes from time as they came under pressure.
Saints looked like they were going to miss out on a bonus point but, with Wasps down to 14 men, substitute scrum-half Martin Roberts scampered over from a scrum with just five minutes left and replacement fly-half Stephen Myler converted.
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