Scrum half and summer recruit Rhodri Williams grabbed a well-worked try on home soil as Dragons made a flying start to the encounter.
But the English side powered back in the second half with a hat-trick from hooker James Fish seeing them go clear in the final stages.
Dragons made six changes from the side that defeated Ealing Trailfinders last weekend, with Jack Dixon captaining while Richard Hibbard made a first start on home soil.
Wales international Dan Biggar and James Haskell made their first appearances of the season for Saints.
The Dragons flew out of the traps with fly half Josh Lewis slotting an early drop goal to reward home pressure.
The Dragons were really impressing with their physicality with a thunderous tackle from skipper Dixon popping out the ball before midfield partner Adam Warren flew away and fed wing Goodchild.
Early home pressure was rewarded further on 12 minutes when the ball was spun down the line to Rhodri Williams who cut back inside and dived over from close range.
Dragons were playing a high tempo game to keep the visitors pinned back. And when they did kick in behind, elusive full back Jordan Williams showed his quick feet to break from deep and start a counter.
Saints started to shuffle their pack to try and get a foothold in the game, but it was wing Ken Pisi who started the comeback as he picked off a pass inside the home half for an interception score.
Five minutes later Saints struck in identical fashion as scrum half Cobus Reinach flew out the line to take a pass and race over unopposed from 60 metres.
The home pack looked to respond with a big driving maul before a turnover forced Rhodri Williams to show all this pace to tear back and cover the danger.
A late charge from the Dragons saw Williams again turn Saints with a great grubber kick for George Gasson, but the visitors held out to take a four-point lead into the break.
Back row Aaron Wainwright stopped early pressure at the start of the second half, as he ripped ball and rattled up field before solid defence won a knock-on to halt mounting Northampton pressure.
But there was nothing the home pack could do when Saints powered over for a third try from a driving maul and then added another in similar fashion when David Ribbans went over.
Dragons showed plenty of heart and battled back with Tiaan Loots and Dafydd Howells combining down the short-side before Tyler Morgan crashed into contact.
The home side opted to kick for the corner from the resulting penalty, but Saints were refusing to be breached.
And, after holding firm under huge pressure, the Saints had the final word with two late scores from Fish.
Timeline:
05m Lewis dg 3-0
12m R Williams t Lewis c 10-0
25m Pisi t Biggar c 10-7
30m Reinach t Biggar c 10-14
46m Fish t Grayson c 10-21
60m Ribbans t Grayson c 10-28
76m Fish t Grayson c 10-35
78m Fish t Grayson c 10-42
Dragons: 15 Jordan Williams (Howells 61), 14 Joe Goodchild, 13 Adam Warren (Morgan 61), 12 Jack Dixon (Loots 49), 11 George Gasson (Will Talbot-Davies77), 10 Josh Lewis (Botica 49), 9 Rhodri Williams (R Davies 49 (R Williams 73)); 1 Ryan Bevington (Ellis 40), 2 Richard Hibbard (Lawrence 40), 3 Brok Harris (Fairbrother 40), 4 Matthew Screech (Nansen 49), 5 Rynard Landman, 6 Aaron Wainwright (Taylor 49), 7 Nic Cudd, 8 Lewis Evans (Benjamin 49)
Replacements: 16 Rhys Lawrence, 17 Gerard Ellis, 18 Lloyd Fairbrother, 19 Brandon Nansen, 20 Huw Taylor, 21 Rhodri Davies, 22 Jacob Botica, 23 Tiaan Loots, 24 James Benjamin, 25 Tyler Morgan, 26 Dafydd Howells, 27 Will Talbot Davies.
Saints: 15 Tom Collins, 14 Ollie Sleightholme, 13 Fraser Dingwall, 12 Piers Francis, 11 Ken Pisi, 10 Dan Biggar, 9 Cobus Reinach; 1 Francois van Wyk, 2 Mikey Haywood, 3 Ehren Painter, 4 Api Ratuniyarawa, 5 James Craig, 6 James Haskell, 7 Lewis Ludlam, 8 Paddy Ryan
Replacements: 16 Alex Waller, 17 Will Davis, 18 James Fish, 19 Joe Gray, 20 Ben Franks, 21 Courtney Lawes, 22 David Ribbans, 23 Luther Burrell, 24 Jamie Gibson, 25 Heinrich Brussow, 26 Mitch Eadie, 27 Alex Mitchell, 28 James Grayson, 29 Nafi Tuitavake, 30 Rory Hutchinson, 31 Matt Worley, 32 Tom Emery
Referee: Adam Jones
Attendance: 3,331
