The Dragons claimed a remarkable victory in heart-stopping fashion at Scotstoun to record back-to-back away wins in the Guinness PRO14.
It looked as though they were going to be denied at the death when replacement hooker Johnny Matthews went over for Glasgow in the 84th minute.
But, from pretty much in front of the posts, South African fly-half Brandon Thomson inexplicably hit the woodwork with the conversion which would have won the match.
That signalled scenes of wild celebration from the Dragons, who have now followed up last week’s victory over Benetton in Treviso to go above Glasgow in Conference A.
Dean Ryan’s team claimed tries from wing Jared Rosser and prop Brok Harris, with outside-half Sam Davies adding 13 points via his trusty left boot.
They opened the scoring after just five minutes and what a fine effort it was.
From a lineout, Jamie Roberts ran a decoy line and Davies gave an inside pass on half way to Rosser, who marked his 50th appearance for the region in style.
The young winger showed blistering pace as he scorched between back three men Glenn Bryce and Niko Matawalu, making the line despite being brought down by a high tackle from Matawalu.
Davies added the conversion and a penalty, but the first half was to see two yellow cards for the visitors, with Harrison Keddie infringing at a ruck near his own posts and Jack Dixon guilty of a no-arms shoulder charge.
While centre Dixon was in the bin, Glasgow struck twice to take a 14-10 interval lead, with flanker Fotu Lokotui rounding off a driving lineout and then scrum-half Sean Kennedy supporting a break from Nick Grigg.
The Dragons went back in front early in the second half as veteran prop Harris ploughed over from close range, with the boot of Davies keeping them ahead as they moved into the final quarter.
Then came a sustained late onslaught from Glasgow and that dramatic finale.
Glasgow: F Lokotui, S Kennedy, J Matthews; cons - P Horne (2); pen - P Horne.
Dragons: Tries - J Rosser, B Harris; conversions - S Davies (2); pen - S Davies (2); drop goal - S Davies.
