Stand-off Ryan Lamb booted 20 points as the Saints turned on the style after the interval to overturn a 10-6 half-time deficit at Rodney Parade on Sunday.
Flanker Phil Dowson and wing Jamie Elliott got the visitors' tries.
Northampton included England stars Lee Dickson at scrum-half and flanker Dowson for a clash they had to win after losing to Harlequins in the last play of the match a week ago.
The Dragons put out an almost identical side from that which lost at Bath's Recreation Ground.
But there was little between the teams in the opening stages, although the Dragons did find themselves under the most pressure.
Lamb could have put his side in front within moments of the kick-off but his straightforward penalty from in front of the posts went wide.
However, the Dragons - near the bottom of the RaboDirect PRO12 - actually got over the try-line first against Northampton - fifth in the Aviva Premiership - when wing Will Harries stormed in from 20 metres, but the pass to him from stand-off Dan Evans was ruled as forward.
Lamb eventually got the scoreboard ticking over on 13 minutes when he landed a 25-metre penalty and Northampton could have gone further clear when Elliott crossed on the left but was adjudged to have had a foot in touch.
But the Dragons would not lay down as their defence held firm and they made some decent inroads to the visitors' territory again.
From an error on halfway by Northampton, Tom Prydie booted a 49-metre penalty to draw the Welsh region level.
However, as happened last week to the Dragons, they returned the points almost immediately as a mistake 20 metres from their own posts saw Lamb land his second kick.
The Saints were counting the bruises of some thumping home tackles as well. Dragons hooker Steve Jones hit down Keri Pisi to save a try on the right, while centre Pat Leach left Dominic Waldouck battered in midfield.
And five minutes from the break, the Dragons got a deserved try with a beautiful move inside the Saints 22 from first phase.
Good line-out ball saw Evans deliver a midfield pass to centre Ashley Smith. He heard Chavhanga call for an offload and, when he obliged, the South African flyer stormed between Waldouck and fellow centre Luther Burrell to go over under the posts, making Prydie's conversion simple.
And it looked like it would not be Lamb's day as another seemingly simple penalty on the stroke of half-time went wide, leaving the Dragons 10-6 ahead.
Lamb reduced the arrears to a point but a horrible mistake inside his own 22 by the stand-off, where he chipped the ball straight to waiting Dragons hands, saw Chavhanga get his second touchdown.
The ding-dong battle took another twist when Dowson got under a pile of bodies to notch Saints' first try. Lamb's conversion put them ahead by a point.
That proved the turning point as another six points from Lamb plus a try from Elliott sent Saints 12 points clear.
And with Dragons replacement Nathan Buck sin-binned for a ruck infringement, there was no way back.
Chavhanga grabbed his hat-trick try nine minutes from the end but a Lamb drop-goal put Northampton out of sight.
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