Saints rediscovered the attacking spark which had deserted them in their opening game to run in six tries, scoring over 16 points for the first time since July last year.
Bradford meanwhile will have to improve dramatically on this showing to stand any chance of reaching the play-offs.
Saints looked dangerous early on and it was no surprise when Wilkin was able score under the posts after taking in Wellens’ offload.
Eastmond converted and then slotted a penalty minutes later to put the visitors firmly in control at 8-0.
Bradford’s play was almost amateurish at times and they were made to pay when Pryce opened up the defense to give Wellens the opportunity to cross the line for his first.
The Pryce-to-Wellens combination added another try before half-time leaving the Bulls looking down the barrel of a second defeat from their opening two games.
To their credit, Bradford started the second half much stronger but could find no way over the line as Saints defended resolutely.
They were creating opportunities and it looked like a Bradford try was inevitable when they forged a huge overlap near the line only for Kyle Eastmond to pull off a last gasp, one handed intercept before racing the length of the field for a thrilling score.
A combination of shoddy handling and desperate defense was keeping Bradford scoreless despite the fact that they were dominating both territory and possession.
After being penned in their own half for almost the entirety of the first 25 minutes of the second half, Saints gave the Bulls a lesson in how to clinically finish as they sensationally kept the ball alive to eventually give Wellens his hat-trick.
And the full-back forward-rolled his way over the line for a fourth try when Matt Gidley offered him the ball in space to extend the lead to 38-0.
Bradford had been continually thwarted by sloppy finishing but they avoided being nilled with the last play of the match as Matt Orford went over to give the Bulls some consolation.