And Northampton, who had previously lost all eight Gallagher Premiership home games in 2020 and who had not won anywhere since beating London Irish at The Stoop in August, finished the job with Mike Haywood pocketing a late bonus-point score.
A penalty try had set the Saints on their way and Mitchell's finish from a fine breakaway gave them a 17-7 half-time lead, with Billy Searle having scored and converted for Worcester.
Searle notched a penalty after the break but Northampton pushed on and Biggar returned from the sin-bin to score before Haywood ensured it was a maximum haul.
Biggar had kicked off his eventful evening by landing an early penalty, but Worcester then threatened as Perry Humphreys tried to find Searle, who knocked on from a pass that was not where he wanted it.
The Worcester full-back was sent to the sin-bin and Northampton were awarded a penalty try, earning them a 10-0 lead.
Biggar sent a penalty just wide soon after and Northampton then stopped a Worcester lineout drive before Nanai returned to the field.
But the Warriors did cross the whitewash when Searle finished from what Northampton felt was a forward pass after a flowing move.
Searle converted but the Saints struck back almost immediately as Biggar sliced through Worcester and released Mitchell for the score.
Worcester cut the 10-point deficit early in the second half thanks to a Searle penalty, which came after Biggar had been sin-binned for killing the move following a big break from Warriors lock Justin Clegg.
Northampton threatened to respond when David Ribbans flew towards the line but he was deemed to have been held up and Worcester escaped.
The Saints were given a reprieve of their own as Worcester broke well but Nick David knocked on with the line in sight just before Biggar returned to the field.
And the fly-half had an instant impact, with Mitchell returning the first-half favour as he sent the Wales star in for a timely score.
Biggar converted and Northampton led by 14 points with as many minutes to go.
And the hosts still had time to bag the bonus point as Haywood powered over in the final minute of the match.