Roared on by a sell-out crowd, Glasgow scored a come-back bonus point 32-10 win after they had trailed 10-6 to Ulster at half-time.
With both sides having already qualified for the play-offs, the outcome means the two teams meet again in Glasgow
With a powerful wind behind them Ulster had the better of the first half scoring a maul-over try through flanker Chris Henry, converted by stand-off Ian Humphreys, who added a penalty.
Glasgow were slow into things from the restart but following a wonderful individual try from full-back Stuart Hogg after 56 minutes, three more followed in a 12 minute period through Richie Vernon and a couple from Finn Russell, who converted all three.
Ulster kicked off in bright sunshine but Ian Humphreys was deceived by the gusting wind and the ball failed to go 10 metres.
Glasgow took the advantage to camp in the visitors’ 22 and went ahead in the fifth minute with a penalty from Russell.
However it was the last time in the half that Ulster failed to harness the wind at their backs.
With Glasgow put on the back foot they conceded half a dozen penalties between the 24th and 29th minutes, the last one seeing lock Jonny Gray dispatched to the sin bin.
The Glasgow defence now cracked and Ulster’s pack drove over from a close-in line out with captain and flanker Chris Henry awarded the try, converted by Humphreys.
It then became Ulster’s turn to foul fall of referee Ian Davies with four penalties awarded, the final one allowing Russell to claw back three points.
However Glasgow then offended at the restart with Humphreys landing the penalty that stretched the visitor’s lead at the break to 10-6.
Among a number of blood injuries Ulster lock Franco van der Merwe suffered a serious one, replaced in the 19th minute by Iain Henderson.
By the restart the wind had fallen away and Glasgow were making little of things until Hogg stepped in with a wonder try in the 55th minute to give them the lead.
A long pass from Russell found him just over half way. He accelerated to the Ulster 22, chipped perfectly, gathered and scored in the corner.
Not to be out-done Russell produced his own try from the same category brushing off several Ulster tackles to score by the posts and then to convert.
Now rocking Ulster had prop Andrew Warwick, playing his first game since January, sin-binned in the 64th minute.
Six minutes later Russell made it a brace, side stepping over after huge Glasgow pressure and converting.
Two minutes later Glasgow had the all-important bonus point when centre Vernon broke a tackle on the Ulster 22 to score with Russell adding the extras.