Wilson's double plus 14 points from the boot of Stephen Myler eased the Saints past a Wasps side who dominated possession in the first half.
It could have been worse for Wasps as Tim Payne was lucky not to receive a red card after television match official Trevor Fisher was called upon by referee Dave Pearson. Replays showed the England loosehead dropping a knee on Vasily Artemyev in a ruck, but he was given just 10 minutes in the sin-bin.
Wasps, who have not won at Franklin's Gardens since November 2005, also saw wing James Bailey - a summer signing from Lyon - carried off on a stretcher with a broken leg 17 minutes into his first start for the club.
The two incidents hampered Wasps' efforts to break a well-drilled Northampton defence and, despite keeping the ball for large chunks of the opening 40 minutes, they turned around 14-6 down.
After five minutes of solid defending, Northampton scored with their first attack and it took just two passes. A poor kick landed in Wilson's lap on his 10m line. He passed to Ken Pisi, who burst through the Wasps line and then passed back to Wilson for the full-back to run over unopposed from 20 metres. Myler missed the conversion and a penalty, but at the third attempt made it 8-0 after 12 minutes.
Nicky Robinson got Wasps on the scoreboard with a penalty after a burst from Christian Wade had got the visitors into Northampton's 22.
But Wasps were dealt a blow when Bailey was carried off on a stretcher.
That said, it did not put them off their stride as they continued to dominate possession and a 15m lineout drive gave Robinson another three points.
Myler replied with three of his own, though, and - after Northampton lock Samoa Manoa showed his side-stepping abilities to nip past a couple of Wasps tacklers - the fly-half made it 14-6.
On the stroke of half-time Payne was sent to the sin-bin after the TMO was called on. Replays showed Payne dropping his knee on Artemyev and the home crowd were furious the England loosehead did not receive a red card.
With Wasps a man down Northampton went for the kill but twice Artemyev, now with his head bandaged, could not gather offloads inches from the try-line and Soane Tonga'uiha could not quite reach the line after charging out of a ruck five metres from the line.
The visitors did well to survive the 10 minutes, although Payne's return did not alter the course of the second half. It was all Northampton.
Northampton lock Christian Day became the second player to be carried off on a stretcher on 55 minutes with his right lower leg strapped up, but it did not stop the hosts' momentum.
And a minute later Wilson squirmed over for his second despite being seemingly stopped on the line by James Haskell and Andrea Masi after a powerful run and offload from Saints centre Luther Burrell.
Worryingly for England and Northampton, Courtney Lawes then limped off and Dylan Hartley came off with some sort of blow to the head.
But Northampton were able to bring Brian Mujati off the bench and the South African tore Wasps' scrum to pieces, winning penalty after penalty to give the home side control as they maintained their impressive start to the season.
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