Bath were on the back foot early on when they conceded a penalty try, with Luke Arscott sent to the sin bin for deliberately knocking the ball down from an offside position.
Calum Clark went over unchallenged in the 14th minute as Northampton opened up a 14-0 lead, before David Wilson powered his way across the whitewash to reduce the deficit after Arscott had returned to the action.
Fly-halves Stephen Myler and George Ford then traded penalties to send the sides in at half-time with the scores at 17-10.
Northampton surged clear after the interval, with Ben Foden teeing up Christian Day in the 47th minute before Ken Pisi sealed the bonus point.
However, despite trailing 31-10, Bath - still awaiting the arrival of cross-code signing Sam Burgess from South Sydney Rabbitohs - refused to lie down.
Tries from Olly Woodburn and replacement Nick Auterac, along with the extras from the boot of Ford, saw Bath haul themselves to within seven points of their hosts, but Mike Ford's men were unable to complete the comeback in the final 10 minutes.
The result saw Northampton climb above Bath to second in the Premiership standings, two points short of new leaders Saracens, who overcame the absence of injured number 10 Owen Farrell to pick up a 40-19 win over Sale Sharks.
The vastly experienced Charlie Hodgson proved to be an able deputy to Farrell as he contributed 15 points during a first half that saw Saracens run in three tries.
Richard Barrington's second-half try earned his side a bonus point, while Sale failed to build on their first win of the season against London Welsh last time out.
Saracens captain Bob Barritt limped off with a calf injury after 13 minutes, but director of rugby Mark McCall stressed he did not believe the issue was serious.
Shane Geraghty kicked 17 points as London Irish registered an impressive 22-19 win at Leicester Tigers - their first triumph at Welford Road for 11 years.
In Sunday's matches, Newcastle Falcons remain winless following a 35-18 defeat at London Wasps, while Exeter Chiefs maintained their promising start with a 36-13 win over Harlequins.
The weekend had kicked off with Gloucester claiming a 46-10 win at beleaguered London Welsh on Friday.