Despite an error strewn first five minutes, and the eighth minute loss of Jason Tovey with a right hamstring strain, the Dragons gave the home fans something real to shout about as they picked up the pace of their game and scored 23 points in a blistering opening half performance.
With back row dynamo Gavin Thomas driving forward at every opportunity, and scrum half Wayne Evans picking out runners at will, the visitors spent all half defending. The reward for the Welsh region came in the shape of tries from flanker Robin Sowden-Taylor and wing Aled Brew.
The first came from an expertly orchestrated close range line-out rumble, while the second was down to quick recycling and non-stop running. It was the kind of honest endeavour and enthusiasm that turned Rodney Parade into one of the toughest grounds to visit in the Magners League last season.
There should have been a third try before the break when replacement outside half Matt Jones kick-passed cross field for Brew, but the ball ran out of play rather than sit up for the man of the match winger.
Jones chipped in with two conversions and a penalty - Tovey had opened the scoring before his departure - and that left the Dragons in complete control at 23-3 at the break.
The Warriors' cause wasn't helped by the sin-binning of lock Tom Ryder just before Brew's try and they also lost Canadian international wing DTH van der Merwe for a petulant attack on Brew in the second half.
Warriors coach Sean Lineen made a raft of changes at half-time and his side at least came out of their defensive shell in the second half. Lock Richie Gray stretched out to score a try that owed everything to Richie Vernon's early break five minutes after the re-start and that gave them new impetus.
Ruaridh Jackson hit the post with his conversion attempt, but then knocked over his second penalty of the game from five metres inside his own half to cut the gap to 12 points.
After that, though the Dragons regained some of their composure and never looked like losing their grip on the game. The final scoreline of 23-11 will give them a timely boost ahead of their trip to the Cardiff City Stadium on Saturday to face the Blues in one of Welsh rugby's big derby clashes.
Dragons: Tries: R Sowden-Taylor, A Brew; Cons: M Jones 2; Pens: M Jones 2, J Tovey.
Glasgow Warriors: Try: R Gray; Pens: R Jackson 2.
Newport Gwent Dragons: Matt Evans; Will Harries, Tom Riley, Patrick Leach, Aled Brew; Jason Tovey (Matt Jones 8), Wayne Evans (Nicky Griffiths 66); Hugh Gustafson (Ali McKenzie 72), Steve Jones (Lloyd Burns 41), Nigel Hall (Pat Palmer 60), Luke Charteris (captain, Rob Sidoli 58), Scott Morgan, Danny Lydiate, Robin Sowden-Taylor, Gavin Thomas
Glasgow Warriors: Bernardo Stortoni (captain); DTH van der Merwe, Max Evans, Graeme Morrison, Federico Aramburu (Hefin O'Hare 41); Ruaridh Jackson (Duncan Weir 57), Henry Pyrgos (Colin Gregor 41); Jon Welsh (Ryan Grant 55), Fergus Thomson (Pat MacArthur 55), Ed Kalman (Moray Low 41), Tom Ryder (Aly Muldowney 57), Richie Gray, Chauncey O'Toole (Rob Harley 41), Calum Forrester, Richie Vernon (Rob Harley 32-41)
Referee: Carlo Damasco (Italy)