Opening night at the new-look Ravenhill provided the drama everyone had anticpated, except for the result the home support had wanted.
Ulster had dominated most of the match and even having missed three clear try scoring chances looked to be heading for a deserved win.
But the only try of the game right at the death from replacement Chris Cuister left the Scots a point behind and British Lion Stuart Hogg converted to give his side a 13-12 victory.
It was more than a flattering win for Glasgow, but Ulster had only themselves to blame after failing to turn their chances into points.
Paddy Jackson kicked four first half penalties to give Ulster a 12-6 interval lead, with Hogg kicking two from three.
Michael Allen and Luke Marshall then dropped passes when tries were on the cards for Ulster and David McIlwaine failed to ground the ball when he got over the line.
Jasckson missed a penalty 10 minutes from time, which would have put Ulster nine points ahead and the game probably safe.
Then, with Glasgow down to 14 men after replacement Moray Low was sinbinned the visitors took Ulster by surprise and scored with that last gasp try with replacement James Eddie going over the try and Hogg adding the extras to snatch the victory
ULSTER: Jared Payne, David McIlwaine, Darren Cave, Luke Marshall, Michael Allen, Paddy Jackson, Ian Porter; Callum Black, Rob Herring, Declan Fitzpatrick, Johann Muller (capt), Dan Tuohy, Roger Wilson, Sean Doyle, Nick Williams.
Replacements: Niall Annett, Tom Court (Black 62), Ricky Lutton (Fitzpatrick 62), Iain Henderson (Muller 59), Chris Henry (Doyle 62), Paul Marshall (Porter 59), James McKinney, Ricky Andrew
Scorers: Jackson (4P)
GLASGOW: Stuart Hogg, Tommy Seymour, Sean Lamont, Mark Bennett, DTH van der Merwe, Ruaridh Jackson, Henry Pyrgos (capt.), Ryan Grant, Pat MacArthur, Ed Kalman, Tim Swinson, Jonny Gray, Rob Harley, Tyrone Holmes, Josh Strauss.
Replacements : Dougie Hall (Macarthur 56), Gordon Reid (Grant 70) Moray Low (Cameron 59), Chris Fusaro (Holmes 56), Richie Vernon (Strauss 56), Chris Cusiter (Pyrgos 66) Gabriel Ascarate (Lamont 56), James Eddie (Harley 74).
Scorers: Eddie (IT) Hogg (2P 1C)
Ref: Ian Davies (WRU)
News Letter man of the match: Ian Porter