Glasgow ran in eight tries in a record away win against an outclassed Dragons team at Rodney Parade.
Mark Bennett, Niko Matalawu and Alex Dunbar's first-half tries put Glasgow in control. In the second half Taylor Paris, Fraser Thomson, Josh Strauss and Tim Swinson (2) added touchdowns.
Duncan Weir converted five and kicked two penalties. Wight converted two.
Tom Prydie's solitary penalty was scant consolation for the Dragons who posted their heaviest ever league defeat.
The Warriors were simply too good for their hosts, quicker in thought and deed and impressive in all facets of play.
It was a record league win for the Scots, and the biggest away win in the Pro12 tournament's history.
The Dragons started well and were ahead inside two minutes as Prydie kicked a penalty, which Weir wiped out within a minute as the Dragons transgressed at the breakdown.
Prydie missed a fairly straightforward penalty in the 12th minute, which Glasgow took as a cue to step up the tempo.
They appeared to blow a chance wide on the left, but the forwards kept control and their patience was eventually rewarded as centre Bennett dummied his way over for the opening try, which Weir converted.
Three minutes later Glasgow increased their lead as right wing Matalawu - a late replacement for Byron McGuigan - beat Prydie to a high bouncing ball from Henry Pyrgos' kick and stretched out to touch down. Weir was again on target with the conversion.
Weir extended the lead with his second penalty in the 27th minute after Prydie's late challenge on Matalawu.
Glasgow were much the better side, with scrum-half Pyrgos calling the shots behind a dominant pack, and stretching the Dragons every time they had possession.
So it was no surprise when the visitors stretched their lead before half time as Alex Dunbar took an inside pass from Weir and spun out of Wayne Evans' despairing tackle to touch down between the posts. Weir converted.
The Dragons started the second half with more purpose, with the forwards driving deep into the Glasgow 22, only to see the ball knocked on by scrum-half Jonathan Evans.
And they paid for their inaccuracy when Glasgow claimed a bonus point just before the hour, Dunbar making the initial thrust and replacement Paris shrugging off some poor tackles to score with his first touch of the match. Weir converted again.
Glasgow's dominance yielded a fifth try when lock Swinson touched down after the pack drove over from a lineout, with Weir converting impressively from wide out.
The Dragons' resistance wilted with Strauss rounding off a sweeping move for a sixth try, with Wight converting, then Swinson brushed aside more half-hearted tackling to score his second.
And Thomson claimed Glasgow's eighth try, which he also converted to round off a miserable night for the Dragons.
Newport Gwent Dragons: Dan Evans, Will Harries, Pat Leach, Jack Dixon, Tom Prydie, Steffan Jones, Jonathan Evans, Ieuan Jones, Nic Cudd, Lewis Evans (captain), Adam jones, Ian Nimmo, Nathan Buck, Hugh Gustafson, Owen Evans.
Replacements: Sam Parry, Aaron Coundley, Nathan Williams, Josh Tyler, Jevon Groves, Wayne Evans, Adam Hughes, Hallam Amos
Glasgow Warriors: Peter Murchie, Niko Matalawu, Mark Bennett, Alex Dunbar, DTH van der Merwe, Duncan Weir, Henry Pyrgos; Gordon Reid, Pat MacArthur, Jon Welsh, Tim Swinson, Tom Ryder, James Eddie, John Barclay, Ryan Wilson (captain).
Replacements: Gerwyn Price, Ofa Fainga'anuku, Ed Kalman, Jonny Gray, Josh Strauss, Taylor Paris, Scott Wight, Fraser Thomson
Referee: Claudio Blessano (FIR)
Assistant Referees: Ian Davis, Rhys Thomas (both WRU)
Citing Commissioner: Aurwel Morgan (WRU)
TMO: Neil Ballard (WRU)