Saracens edged an entertaining Heineken Cup pool contest at Wembley but a bonus point kept Ospreys in contention.
Sarries led 10-3 after an early Rhys Gill try before the first of Ashley Beck's two scores saw the Welsh region level.
But Saracens led 23-13 at the interval after a second try from Ernst Joubert and three Owen Farrell penalties.
Chris Wyles' try put them 28-16 up but Beck's second and Dan Biggar's fourth penalty rewarded the visitors' efforts.
The two sides will meet again at the Liberty Stadium in Swansea next Friday with qualification still very much up for grabs, Treviso's victory over Biarritz earlier in the day leaving the pool wide open.
Sarries started with a bang and almost sent Wyles sliding in at the left corner inside two minutes, Richard Fussell just bundling the wing into touch.
But the Premiership champions didn't have long to wait. A minute later Joubert stole an Ospreys line-out and Welsh prop Gill was driven over under the posts, Farrell converting.
Biggar and Farrell exchanged penalties before Ospreys hit back with a cracking try from deep.
Opting to counter from their 22, Tommy Bowe latched onto a grubber kick and when he off-loaded, Beck picked up a fortunate bounce and fended off Charlie Hodgson to race home.
Biggar's conversion levelled the scores but Ospreys were left feeling aggrieved when French referee Pascal Gauzere brought another promising attack to a halt for a forward pass, which was questionable at best.
Saracens wheeled the ensuing scrum and number eight Joubert slipped out of a poor tackle from Ospreys captain Tom Smith to power over, Farrell adding the extras.
Biggar's second penalty made it 17-13 but Farrell responded with another of his own in the 34th minute to give Sarries a seven-point cushion.
The Ospreys' plight worsened three minutes before the interval when Smith was sin-binned for entering the side of a ruck, and when Biggar was penalised for a high tackle, Farrell extended the hosts' advantage to 10 points.
The visitors swiftly got back into losing bonus-point range on the resumption with another Biggar penalty.
But Sarries had the extra cutting edge in attack, the depth of their runners yielding a third try when an exquisite reverse pass from hooker Schalk Brits out the back of his hand sent Wyles over.
Smith's return saw Ospreys back up to a full complement of 15, but Biggar was off target with two further penalty chances, the second from halfway.
Saracens were then reduced to 14 men when Farrell - a contender for England's Six Nations squad next month - was sin-binned for a cynical check on Biggar as the fly-half chased his own chip ahead.
The Ospreys took advantage of the extra man, exploiting space down the blind-side as Fussell sent Beck in for his second try.
Farrell's first act on his return was to miss a kickable penalty, having moved to fly-half in place of Charlie Hodgson, with former Munster scrum-half Peter Stringer entering the fray for his debut.
But Farrell made no mistake from in front of the posts with seven minutes left, only for Biggar to bring Ospreys back within bonus-point range after Rhys Webb had charged down a Farrell clearance.
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: Jamie George (for Brits, 49), Deon Carstens (for Gill, 73), Carlos Nieto (for Stevens, 65), George Kruis (for Botha, 58), Andy Saull (for Burger, 65), Peter Stringer (for Spencer, 59), James Short (for Hodgson, 59).
Not used: Adam Powell
Sin Bin: Farrell (48).
Ospreys: Richard Fussell; Tommy Bowe, Andrew Bishop, Ashley Beck, Shane Williams; Dan Biggar, Rhys Webb; Duncan Jones, Richard Hibbard, Adam Jones, Ryan Jones, Jonathan Thomas, Tom Smith (capt), Justin Tipuric, Joe Bearman.
Replacements: Huw Bennett (for Hibbard, 48), Ryan Bevington (for D Jones, 48), Ian Gough (for Smith, 53), George Stowers (for Bearman, 58).
Not Used: Aaron Jarvis, Tom Isaacs, Matthew Morgan, Sonny Parker.
Sin Bin: Smith (37).
Referee: Pascal Gauzere (France).