Gregor Townsend’s men scored four second half tries against an Ulster side that saw 12 changes due to injury and squad management.
Glasgow made a strong start playing into the stiff breeze and after a sustained period of pressure, Finn Russell opened the scoring with a fifth minute penalty after Ulster were caught offside.
Ulster however, fought their way back into the game and were unlucky not to get the opening try on 13 minutes. Following a strong scrum Paul Marshall chipped over the defence, but Tommy Seymour won the race to touch the ball down over the goal line.
Ulster were dealt a blow when South African lock Franco van Der Merwe had to come off injured, however Ulster started to dominate.
From a penalty kicked to touch Louis Stevenson was stopped just short but Ulster were awarded another penalty and put together a slick passage of play.
Stevenson again made hard yards, Iain Henderson had a drive, Ian Humphreys then took it on, Louis Ludik and Stuart McCloskey took it close to the line, Clive Ross was held up close to the line before prop Andy Warwick tried to wriggle over but lost the ball over the try line.
Ulster were awarded a penalty and Marshall caught the home defence were he took a quick tap. Henderson and McCloskey drove close to the line and when it was illegally stopped Glasgow lock Jonny Gray was sin-binned.
Ulster kicked the resulting penalty to touch and from the lineout following a perfectly executed driving maul captain Chris Henry was propelled over for the game’s opening try with Humphreys converting.
Russell added his second penalty on 36 minutes after Ulster were caught offside in front of their posts.
Humphreys landed a penalty in the last minute of the first half to give Neil Doak’s side a 10-6 lead at the interval.
Glasgow took the lead for the first time with a try from full back Stuart Hogg.
Russell threw a long speculative pass to the wing, Hogg did well to catch and he chipped through and had enough pace to win the race. He kept his composure to slide over in the corner but the home outhalf missed the conversion.
Glasgow got their second try on 60 minutes.
Russell got the ball in midfield and with seemingly nothing on he was able to take advantage of missed tackles in the Ulster defence to touch down and he was able to convert his own try.
Ulster’s cause wasn’t helped when Warwick came in from the wrong side to pull down a ruck and received a yellow card.
Glasgow nearly made Ulster pay immediately when following a slick backs move Gray was held up over the Ulster try line.
Down to seven men in the scrum, Glasgow were able to force a series of penalties, they decided then to take a quick tap and with an overlap Russell was able to go over unopposed for his second try on 70 minutes and he added the simple conversion.
Glasgow sealed their home semi final on 72 minutes with a fourth try.
Ryan Wilson made a break before releasing centre Richie Vernon to dart over and Russell converted.
Teams
Glasgow Warriors:
S Hogg; T Seymour, R Vernon, P Horne, S Lamont; F Russell, N Matawalu;
R Grant, D Hall, R de Klerk; J Gray, Al Kellock (c); J Strauss, C Fusaro, A Ashe
Replacements:
P MacArthur, G Reid, M Cusack, L Nakarawa, R Wilson, H Pyrgos, D Weir, P Murchie.
Ulster:
L Ludik; R Scholes, S Arnold, S McCloskey, M Allen, I Humphreys, P Marshall;
A Warwick, R Herring, R Lutton, L Stevenson, F van der Merwe, C Ross, C Henry (c), R Diack
Replacements:
R Best, K McCall, B Ross, I Henderson , R Wilson, R Pienaar, P Jackson, T Bowe.
Ref I Davies WRU