The Dragons came back from a 10-20 deficit to overcome Glasgow 24-23 in their RaboDirect PRO12 meeting at Rodney Parade on Sunday.
The Welsh region headed into the match looking to address a run of three defeats, while the Warriors were seeking to make it a Welsh double following last week's win over Cardiff.
And the visitors made the perfect start to match, going ahead in the second minute when Robert Harley crossed for Finn Rusell to convert.
Jason Tovey narrowed the arrears with a penalty, but the seven-point cushion was quickly restored by Mark Bennett's goal.
But the Dragons were level almost straight from the restart as Owen Evans snapped up a sublime offload to cross for the hosts' first try. Tovey added the goal to make it 10-10.
It remained that way until the closing minutes of the first half when Niko Matawalu broke the home defence for Russell to convert and restore the seven-point advantage.
The first points of the second half came close to the hour, when Russell's penalty but Glasgow even further in front. It left the hosts with a mountain to climb in the fourth quarter, but they were up to the task and emerged deserved winners.
Cory Hill got the comeback up and running when he crossed following a spell of pressure for Rhys Jones to convert, and after the Dragons had been penned back by a Russell penalty on 68 minutes, they snatched the lead when Ross Wardle powered over.
Jones added the crucial conversion to put the hosts a point in front, and they were able to hold on to their slender advantage for the final eight minutes to secure a nail-biting win.
Tries: O Evans, Cudd, Wardle
Con: Tovey, Jones 2
Tries: Harley, Matawalu
Con: Russell 2
Pen: Bennett, Russell 2
Dragons: 15 Rhys Jones, 14 Matthew Pewtner, 13 Pat Leach, 12 Ashley Smith, 11 Will Harries, 10 Jason Tovey, 9 Richie Rees, 8 Lewis Evans, 7 Nic Cudd, 6 Jevon Groves, 5 Cory Hill, 4 Andrew Coombs (c), 3 Duncan Bell, 2 T. Rhys Thomas, 1 Owen Evans.
Replacements: 16 Hugh Gustafson, 17 Phil Price, 18 Bruce Douglas, 19 Matthew Screech, 20 Ieuan Jones, 21 Wayne Evans, 22 Dorian Jones, 23 Ross Wardle.
Glasgow Warriors: 15 Ruaridh Jackson, 14 Lee Jones, 13 Richie Vernon, 12 Mark Bennett, 11 Byron McGuigan, 10 Finn Russell, 9 Niko Matawalu, 8 Josh Strauss (c), 7 Tyrone Holmes, 6 Rob Harley, 5 Jonny Gray, 4 Leone Nakarawa, 3 Mike Cusack, 2 Dougie Hall, 1 Jerry Yanuyanutawa.
Replacements: 16 Fraser Brown, 17 Gordon Reid, 18 Jon Welsh, 19 Tom Ryder, 20 James Eddie, 21 Henry Pyrgos, 22 Folau Niua, 23 Rory Hughes.
Referee: Matteo Liperini (Ita)
Assistant referees: Rhys Thomas, Martyn Lewis (both Wal)