Friday night's game finished with the home side winning by 23 points to six in miserable conditions at Ravenhill, meaning Ulster sealed top spot in Pool Four.
Last year's runners-up celebrated tries from Nick Williams, Jared Payne and Darren Cave plus eight points from Ruan Pienaar.
Pienaar kicked Ulster ahead after seven minutes.
Williams then crashed over for a try from short range to give the province a 10-0 lead going into half time.
Glasgow responded when Duncan Weir scored a penalty on 49 minutes, and after Iain Henderson was sinbinned.
Weir then added a second to reduce the gap to four points.
Pienaar scored a penalty for Ulster on 62 minutes, before tries from Payne and Cave secured the win following a scrappy game in difficult conditions.
Ulster took four points to progress in the competition after Northampton beat Castres.
They travel to face the French side next weekend knowing they have already achieved their first goal of the season by reaching the knock-out stages of the tournament.
Coach Mark Anscombe said: "It's credit to the guys that they've achieved this and that's one thing that we can put down that we've qualified after the fifth round (of matches) for the quarters."
"We set out as a goal this year to make a Heineken quarter-final.
"But we're certainly not resting on it and we're going to Castres next week with a job to do and reward our fans with a home quarter-final.
"I think if we don't do that we'll have let the supporters down a little bit."
The game also saw Andrew Trimble make his 150th appearance for the province.