Parks puts the boot in UlsterGlasgow 25
Ulster remain bottom of the Magners League after a fourth consecutive away defeat as Glasgow inflicted more misery on Mark McCall's men.
Ulster have failed to take a single point away from home and have only managed three tries in four trips outside Ravenhill.
Scottish out-half Dan Parks was Ulster's chief tormentor, scoring 20 points to become the competition's second highest scorer and leave Ulster with serious questions before English Premiership leaders Gloucester arrive in Belfast next Friday for the start of the Heineken Cup.
Parks opened the scoring with a penalty on nine minutes as Neil Best was punished for an off the ball incident and doubled the advantage with his second successful penalty following a good drive from a lineout.
Darryl Gibson's surging run cut open the Ulster defence and as Glasgow recycled Justin Harrison strayed offside to give Parks a simply penalty to extend the lead on 17 minutes.
Ulster then escaped as Parks failed with a drop goal attempt.
Andrew Trimble's tackle on Andy Henderson saved a try as Ulster turned over the ball in their own 22.
More Ulster indiscipline allowed Parks to slot over another penalty on the half hour as the visitors failed to stay on the feet at the ruck.
Ulster should have came away with a try on their first salvo into the Glasgow 22. They kicked a penalty into touch and from the resulting drive Justin Harrison, Andrew Trimble and Neil Best were all stopped short of the line and Parks was able to clear as Ryan Caldwell was turned over.
Mark McCrea nearly scored as Tommy Bowe cut open the home defence and put his winger in the clear, but as he went for the corner Parks was able to get across and force him into touch.
Ulster were dealt a further blow on the stroke of half time as flanker Kieron Dawson was stretched off.
Ulster registered their first points on 45 minutes with a Humphreys penalty as Glasgow failed to roll away form a ruck and he then closed the gap with a second penalty as Glasgow failed to stay on their feet at the ruck.
Parks then showed that he is human afterall as he missed a drop goal in front of the posts as Glasgow began to reassert the pressure.
Johnny Beattie nearly breached the Ulster defence as he picked up at the base of the scrum and went round Neil Best, but he was stopped on the line by some desperate tackling.
Glasgow's sustained pressure finally told on 69 minutes as centre Andy Henderson went over for the game's first try. After a series of phases Sam Pinder gave his centre a flat pass and he had enough strength to hold of Stephen Ferris and Boss to power over with Parks converting.
Late on Trimble was punished for an off the ball incident and Parks knocked over the reversed penalty to seal Ulster's feat.
GLASGOW: B Stortoni, L Fa'atau, A Henderson, D Gibson, T Evans, D Parks, C O'Young, J Va'a, F Thomson, M Low, A Newman, A Kellock (capt), K Brown, J Barclay, J Beattie.
Replacements: E Milligan for Thompson 53 mins , E Kalman for Va'a 57 mins, D Turner, J Eddie, S Pinder for O'Young 57 mins, E Barrow, H O'Hare.
ULSTER: B Cunningham; T Bowe, A Trimble, R Dewey, M McCrea; D Humphreys, I Boss; J Fitzpatrick, R Best, B Young; J Harrison, R Caldwell; N Best, K Dawson, S Ferris.
Replacements: S Philpott, D Fitzpatrick, C del Fava, R Wilson for Dawson 39 mins, K Campbell, P Wallace for McCrea 67 mins, M Bartholomeusz for Cunningham 53 mins.
Referee: A Small (IRFU).