Ospreys (15) 48
Justin Marshall added the Ospreys' second try before half-time
Tries: Parker, Marshall, A W Jones, Tiatia, Walker 2, Byrne
Cons: Hook 5
Ulster (3) 17
Tries: Boss, Danielli
Cons: Wallace 2
The Ospreys moved back into contention in Pool 2 with a seven-try bonus-point Heineken Cup win over Ulster on Friday.
Sonny Parker claimed their first try on five minutes, with Justin Marshall also crossing before half-time.
Alun Wyn Jones, Filo Tiatia, Nikki Walker - with two great wing scores - and Lee Byrne added further tries.
Ulster were limited to a gutsy solo effort from scrum-half Isaac Boss and Simon Danielli's late try, plus seven points kicked by Paddy Wallace.
It took the Ospreys just five minutes to break the Ulster line, as Byrne picked a good line from full-back to send Parker over in the right corner.
James Hook missed the conversion but the fly-half made no mistake seven minutes later with a penalty to stretch the home lead to 8-0.
Ulster's best chance of the opening period came on the counter-attack as Tommy Bowe gathered a long Byrne kick and fed Bryn Cunningham.
The full-back produced the most delicate of chips to gather the other side of the Ospreys defensive line.
But as he raced down the right wing the Welsh cover arrived before the Irish supporting runners and the move petered out on the sideline.
It was the Ospreys who remained on the front foot and a second try soon followed after a concerted period of pressure that took them into the Ulster 22.
Marshall provided the killer blow, a strong hand-off taking the former New Zealand scrum-half under the posts with a ridiculous corkscrew dive and Hook then converting.
Wallace got Ulster on the scoreboard with a penalty, but all too often in the remainder of the half the visitors opted to kick away what possession they had.
The Ospreys started the second half just as they had the first, patiently working their way upfield and scoring within five minutes of the kick-off.
A series of drives sucked in the Ulster defence and prop Duncan Jones popped the pass left for fellow forward Wyn Jones to go over for a 22-3 lead after Hook's conversion.
A fourth try to secure the bonus point soon followed, created by Marty Holah's break and taken on for captain Tiatia to cross the whitewash for another seven-pointer.
Perhaps we were a bit slow of thought at times
Ulster caretaker coach Steve Williams
If the Ospreys thought things were done and dusted they were jolted out of any complacency by Boss claiming a try for Ulster.
The scrum-half jinked his way through a forest of grasping arms to go under the posts, with Wallace's conversion reducing the deficit to 29-10.
Back came Ospreys with the best try of the night, as Walker stood up opposite wing Bowe before the Scot turned on the afterburners to stretch away to the line.
Hook added his fourth conversion to make the score 36-10 with 17 minutes remaining.
Ulster's own Scotland wing Danielli, who had looked the most dangerous of the visiting backs, crossed late on for a deserved consolation try.
However, the Ospreys had the last word with their sixth try as Byrne muscled his way over at the right corner flag before Walker added his second at the death from Shaun Connor's break.
Ulster have a chance for revenge next week in the return at Ravenhill, but will have to improve markedly from this display to salvage pride in a pool in which they are now realistically also-rans.
With Gloucester earning their own bonus-point win out in Bourgoin, the Ospreys probably need a win at Ulster next week to stay in touch with the Cherry and Whites.
Ospreys coach Lyn Jones:
"We are satisfied with the result. It was a good night for us.
"You cannot win the Heineken Cup before Christmas, but you can certainly lose it and we just need to keep the pressure on Gloucester.
"If we can go to Ravenhill next Friday night and beat Ulster then it will set us up for a huge clash against Gloucester in the New Year."
Ulster caretaker coach Steve Williams:
"We were out-gunned and out-powered at times. There is no other option but to roll up our sleeves.
"We have just got to work hard and keep plugging away to get ourselves out of the situation we are in.
"I could not question the players' commitment but perhaps we were a bit slow of thought at times and stood off a little bit in defence."
Ospreys: Lee Byrne; Nikki Walker, Mark Taylor, Sonny Parker, Shane Williams; James Hook, Justin Marshall; Duncan Jones, Huw Bennett, Adam Jones, Alun Wyn Jones, Ian Evans, Jonathan Thomas, Marty Holah, Filo Tiatia (capt).
Replacements: Richard Hibbard for Bennett (46), Cai Griffiths for Adam Jones (69), Ian Gough for Tiatia (53), Ben Lewis for Holah (69), Mike Phillips for Marshall (64), Shaun Connor for S. Williams (74), Andrew Bishop for Parker (65).
Ulster: B Cunningham; T Bowe, A Trimble, P Steinmetz, S Danielli; P Wallace, I Boss; J Fitzpatrick, R Best (capt), B Young, J Harrison, C del Fava, N Best, D Pollock, M McCullough.
Replacements: D Fitzpatrick for J. Fitzpatrick (64), M Miles for R. Best (75), R Caldwell for Harrison (59), K Dawson, K Campbell for Boss (72), N O'Connor for Danielli (70), R Dewey for Steinmetz (59).
Referee: Chris White (England).