Saracens took a huge stride towards the quarter-finals after winning their Heineken Cup clash at the Ospreys.
Back-row Ernst Joubert scored a crucial first-half try, after Charlie Hodgson charged down the kick of dawdling Ospreys fly-half Dan Biggar.
Owen Farrell added the conversion and also kicked three penalties.
Ian Gough went over to give the Ospreys hope, but despite the losing bonus point they are now realistically out of contention for the knock-out stage.
Saracens top Pool Five on 14 points, with Biarritz second on 12 after coming from behind to beat Treviso 29-12 at home, while the Ospreys trail in third on eight points.
The Ospreys lost 31-26 at Wembley last weekend to Saracens and the early signs were that the return at the Liberty Stadium would be equally tight.
Farrell and Dan Biggar exchanged a brace of penalty kicks in an absorbing - and tetchy - first quarter, in which rival back-rows Joubert and Ryan Jones were the men who caught the eye making the hard yards.
But Saracens took control of what had been a tight contest when Biggar took too much time over a clearance, allowing opposite fly-half Hodgson to block the kick.
The ball fell kindly into the arms of the waiting Joubert and the big South African cantered over the line.
Farrell converted the simple kick and added a third penalty before the break for a 16-6 lead.
The half ended badly for the Ospreys, with Biggar continuing his troubles by missing a relatively straightforward penalty and prop Paul James being sin-binned after a series of collapsed scrums.
Biggar began the second half with a second penalty miss, but the fly-half was at least driving his side forward as the Ospreys restarted brightly.
Ashley Beck nearly claimed a try for the home side, after fine sleight of hand from hooker Richard Hibbard.
But the centre was hauled down just short and after the television match official looked at the incident, Beck was instead penalised for a double movement.
Referee Jerome Garces then sin-binned Saracens hooker Schalk Brits after losing patience at the breakdown, signalling a period of sustained Ospreys pressure.
Saracens survived the 10 minutes short-handed but just after the English side were back to full strength, Kelly Brown was yellow carded for tripping Biggar.
This time the Ospreys made their numerical advantage count, with Shane Williams sucking in the cover before Biggar fired a long pass out to Gough lurking on the right.
The lock muscled his way over at the corner flag and Biggar added an excellent touchline conversion to bring the Welsh side to within three points.
Five minutes from the end Farrell missed a penalty that would have rubber-stamped the victory, but the Ospreys were unable to find another score and suffered their first European home loss in 17 games.
Saracens rugby director Mark McCall:
"That was massive for us. We spoke about needing to back up a good performance and a good win last weekend against a good team who were unbeaten on their home park for a very long time and we have done that.
"It was a different game to last weekend. We had to roll our sleeves up and dig in, I have nothing but respect for our group.
"We were down to 14 men for 20 minutes in that second half and they still worked and worked, they are a special group."
Ospreys head coach Sean Holley:
"A couple of errors cost us. To concede a try from a charge down was very frustrating.
"We dominated territory and possession and some errors at crucial moments cost us.
"But full credit to Saracens, they have an outstanding defence and we couldn't break it down.
"I can't fault the effort and attitude of the players, they went for it and didn't leave anything on the field. We couldn't ask much more than to tidy up some bits of accuracy."
Ospreys: Richard Fussell; Tommy Bowe, Andrew Bishop, Ashley Beck, Shane Williams; Dan Biggar, Rhys Webb; Paul James, Richard Hibbard, Adam Jones, Ian Gough, Ian Evans, Ryan Jones, Justin Tipuric (capt), Jonathan Thomas.
Replacements: Huw Bennett, Duncan Jones for James (57), Aaron Jarvis, Joe Bearman for Evans (71), George Stowers for Tipuric (76), Kahn Fotuali'i for Webb (54), Matthew Morgan for Biggar (76), Hanno Dirksen for Fussell (56).
Sin Bin: James (38).
Saracens: Alex Goode; David Strettle, Owen Farrell, Brad Barritt, Chris Wyles; Charlie Hodgson, Ben Spencer; Rhys Gill, Schalk Brits, Matt Stevens, Steve Borthwick (capt), Mouritz Botha, Kelly Brown, Jacques Burger, Ernst Joubert.
Replacements: John Smit for Brits (72), Deon Carstens, Carlos Nieto for Stevens (61), George Kruis for Borthwick (71), Andy Saull for Burger (71), Peter Stringer for Spencer (61), Adam Powell for Hodgson (72), James Short for Wyles (51).
Sin Bin: Brits (50), Brown (63).
Referee: Jerome Garces (France).