Glasgow suffered another Celtic League setback when Ulster battled back to claim a crucial away point at Hughenden.
The 6,000 home fans had been celebrating as they watched their heroes pile up a 16-point lead, thanks mainly to a two-try burst from Gordon Simpson.
Glasgow broke the deadlock after just two minutes when Tommy Hayes slotted a penalty, only for David Humphreys to reply in identical fashion almost immediately.
Simpson's first try came in the 20th minute as he ploughed over after skippper Andy Nicol was held up on the line.
Humphreys kept Ulster in the picture with another penalty but Simpson claimed his second score, converted by Hayes.
Glasgow kept up their momentum and Nicol made up for his earlier near-miss by grabbing the third try. Hayes again slotted the conversion to give his side a 16-point cushion going into the final stages.
Ulster were far from dead, however, and they stunned the home troops with quickfire touchdowns by substitutes Russell Nelson and Ryan Constable - one of which was goaled by Paddy Wallace.
A long-range McLaren penalty earned Glasgow some breathing space, but the contest was squared when Humphreys converted Wallace's late try from the touchline.
GLASGOW: Kiddie; Steel, McLaren, Henderson, McInroy; Hayes, Nicol; Blades, G. Bulloch, Hilton, Ross, White, Simpson, MacFadyen, Petrie. Replacements: Scott, Prescott, Stewart, Flockhart, Black, Stuart, Reid.
ULSTER: Wallace; J Topping, J Bell, Larkin, Howe; Humphreys, Free; Fitzpatrick, Shields, Best, Davidson, Longwell, Allen, Ward, McWhirter. Replacements: Weir, Boyd, Blair, Nelson, K Campbell, Constable, Malone.
Referee: N Whitehouse (Welsh RFU).