Mitch Eadie scored a dramatic late try as Saints surged back from 14-0 down to complete a 15-14 comeback win at the Ricoh Arena on Sunday afternoon.
The black, green and gold looked down and out when Wasps scored their second try eight minutes into the second period, but Saints summoned a response from out of nowhere.
Taqele Naiyaravoro's try breathed life into their victory bid and after applying some late pressure, Eadie finished off the forward push under the posts.
James Grayson easily converted to ensure his side claimed the spoils at a sparsely-populated Ricoh Arena.
The victory ended a run of six successive defeats against Wasps and Saints have now won both of their Premiership Rugby Cup Pool 3 matches so far this season.
Chris Boyd's side had headed to Coventry on the back of a big home win against Bristol Bears on the previous weekend, and they started on the front foot against Wasps.
Saints won plenty of penalties early on, but they were profligate as James Grayson missed touch with one kick to the corner and the ball was lost from a later lineout.
The first 14 minutes had almost exclusively been played in the Wasps half, but with Saints failing to capitalise on their possession, they were made to pay.
Wasps put together a lovely team try that was finished by wing Watson, with Billy Searle converting to make it 7-0.
The home side were boosted by that score, gaining more of a grip of the game and pushing to secure a second try.
Saints had to hold firm from a threatening lineout drive deep in their own territory, and they managed to win the scrum to stop the Wasps momentum.
But the home team kept coming and after winning a succession of scrum penalties five metres from the Saints line, it looked certain that they would score.
However, Saints somehow survived, defending stoically and kicking the ball out to ensure they would end the half just seven points down.
But Wasps picked up where they left off when the second half began, and they finally forced their way over, through WIllis.
Searle converted to make it 14-0, but Saints finally got on the board with 51 minutes gone as Grayson landed a penalty.
The game continued to be an untidy affair but after replacement Alex Coles kicked ahead to put Wasps under pressure, a between-the-legs pass from Grayson helped Naiyaravoro to stroll in out wide.
Grayson missed the conversion, but the gap was now just six points with 15 minutes remaining.
However, Wasps refused to let Saints get any more territory and the home side had a chance to add to their lead when Searle lined up a penalty. But he landed it just short.
Saints had one final chance to grab a dramatic late win, but after kicking to the corner, they lost their chance as Wasps held firm against the drive to win a scrum five metres from their own line.
But the hosts could not hold on and after Saints won a scrum of their own, they used the platform to send push Eadie over under the posts.
Grayson slotted the conversion to ensure all the noise at the final whistle came from the delighted away support.
Wasps: Miller (c); Watson (James 40), Neal, Lovobalavu, Curtis; Searle, Hampson; West (McIntyre 43), Oghre (Harris 36), Cooper-Woolley (Hunt 67); Matthews, Myall (Cardall 67); Morris (Seabrook 77), Atkinson, Willis.
Saints: Furbank (Naiyaravoro 55); Kellaway, Dingwall, Strachan, Sleightholme (Gillespie 72); Grayson, Davies (Tupai 72); van Wyk (Trinder 72), Fish (Marshall 53), Franks (Garside 77); Ratuniyarawa, Barrow (Coles 62); Gibson (c), Ryan (Onojaife 56), Eadie.
Referee: Sara Cox