The English Premiership giants flew out of the traps with early scores from lock David Ribbans and scrum half Alex Mitchell easing them clear.
Dragons then got on the wrong side of referee Matheu Raynal who reduced them to 13 men – with Lewis Evans and Adam Warren yellow carded – and awarded Saints a penalty try before the break.
Hooker Elliot Dee scored just after the break to spark comeback hopes – his third try in two European games.
But Saints duly wrapped up the try bonus through man-of-the-match Ribbans with a close range finish.
Dragons hit back with Jarryd Sage going over before Cobus Reinach scored a long range effort for Saints. The home side were awarded a penalty try on the stroke of full-time.
Head Coach Bernard Jackman made five changes to the side that won convincingly in Romania, with captain Cory Hill recalled to make his 100thappearance.
Aaron Wainwright, Rhodri Williams, Jordan Williams and Jared Rosser were also back in the starting line-up.
However, it was the visitors who made a quick start with a series of penalties pinning Dragons back and Ribbans driving over from close range.
Scrum half Williams looked to fire a response when he intercepted a pass, as Saints threatened again, but he was chased down on halfway.
Rosser was an early injury casualty, replaced by Warren after 11 minutes, as both teams looked to unload some meaty tackles and make a physical impression.
A second away try soon followed, though, as Biggar broke away in midfield and tore down the middle before flicking a pass to half back partner Mitchell to scurry over the whitewash.
Biggar was proving a real menace in attack as he offloaded in the tackle once again, but as Saints went wide at pace they saw captain Alex Waller spill the ball.
Two penalties saw Dragons look to rally and kick to the corner only for Northampton to halt a driving maul.
Josh Lewis then broke away, after Ollie Griffiths secured turnover ball, but his offload failed to find support runners and Northampton won a penalty and the chance to clear.
After a period of sustained home possession, Saints hit back as the penalties piled up and, when Evans was yellow carded by referee Raynal, the visitors looked to make the extra man count.
The very next driving maul was shunted forward with menace before the referee awarded a penalty try and reduced the home side to 13 men with Warren sent to the bin.
Full back Jordan Williams saw a long range penalty pull up short and wide as Dragons went to the dressing rooms 21-0 down and in need of a huge fight-back.
They showed some of the required fight four minutes after the restart as a driving maul was held up and Dee peeled off the back and got the ball down. Lewis added the extras.
But, within five minutes, the visitors struck decisively for the bonus point with Ribbans the man to burrow over for his second of the night.
Dragons continued to battle away and were over for a second when Sage brushed off a tackler and went over, with the officials deeming he was not held.
Northampton scored again with replacement scrum half Cobus Reinbach stripping the ball in the tackle and tearing away to score from 60 metres out.
The final word went to Dragons with two powerful driving mauls seeing referee Raynal award the hosts a penalty try with the final play and yellow carding Reinach.
05m Ribbans t Biggar c 0-7
14m Mitchell t Biggar c 0-14
33m Penalty t 0-21
44m Dee t Lewis c 7-21
49m Ribbans t Grayson c 7-28
63m Sage t Lewis c 14-28
69m Reinach t Grayson c 14-35
80m Penalty t 21-35
Referee: Mathieu Raynal (Fra)