Early tries from centre Sonny Parker, his third in the tournament this season, and scrum-half Marshall put the Ospreys in charge.
Ulster scored tries through Isaac Boss and Simon Danielli but the defeat was their third loss in three matches in Pool 2 this season.
Further tries by lock Alun-Wyn Jones and skipper Filo Tiatia guaranteed the Ospreys’ maximum points to stay in touch with group pace-setters Gloucester who beat Bourgoin 31-7.
Wing Nikki Walker added a fifth touchdown before full-back Lee Byrne and Walker again completed Ulster’s misery, with fly-half James Hook booting five conversions and a penalty.
Ospreys coach Lyn Jones said: “We are satisfied with the result. It was a good night for us.
“You cannot win the European Cup before Christmas, but you can certainly lose it, and we just need to keep the pressure on Gloucester.
Rugby is about confidence, and things are building slowly.” Gloucester made it three wins in three with a bonus-point victory away to Bourgoin.
The English side led 17-0 at half-time thanks to Anthony Allen and James Simpson-Daniel tries.
Ryan Lamb grabbed their third score and although Julien Frier crossed for the hosts, Andy Titterrell grabbed the crucial fourth try in injury-time.
In Pool 6, Leinster beat Edinburgh 28-14 but failed to secure a bonus point in a group which also features former champions Leicester and Toulouse.
Tries from Jamie Heaslip and Keith Gleeson helped the home side into a 18-3 lead by half-time.
John Houston’s try gave Edinburgh hope and the visitors were still within a score of Leinster as Felip Contepomi and Phil Godman swapped penalties.
Contepomi’s try extended Leinster’s lead but the fourth try proved elusive.
Final Score Ospreys 48 Ulster 17
Ospreys (15) 48
Tries: Parker, Marshall, A W Jones, Tiatia, Walker 2, Byrne
Cons: Hook 5
Pens: Hook
Ulster (3) 17
Tries: Boss, Danielli
Cons: Wallace 2
Pens: Wallace
Gloucester club captain Greig Laidlaw will leave the English Premiership Rugby club at the end of the season to join French Top 14 club Clermont. Scotland captain Laidlaw joined...
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