Ulster have missed-out on a place in this season's Guinness Pro12 Grand Final.
Glasgow scored a dramatic late try to snatch a 16 points to 14 victory at Scotstoun.
A first-half try from Chris Henry helped Ulster to lead for the majority of the game.
But Glasgow winger D.T.H Van Der Merwe scored a last-gasp try in the corner in the 75th minute to level the match before out-half Finn Russell held his nerve to score the winning conversion from the touchline.
The Warriors will now travel to Belfast for next week's final where they'll face the winners of tomorrow's semi-final clash between Munster and the Ospreys.