Saracens beat Ospreys to keep alive their hopes of retaining the European Champions Cup - despite playing for 75 minutes with 14 men.
Rhys Carre was sent off after just five minutes for a shoulder-led tackle on Dan Evans, who scored the first half's only try as Ospreys trailed 12-10.
Evans crossed early into the second half to put the hosts ahead but Saracens reclaimed the lead with Alex Lewington's try.
Manu Vunipola's fifth penalty sealed victory for Saracens, who move up to second place in Pool Four.
That could change when leaders Racing 92 host Munster in Paris on Sunday (15:15 GMT).
For Ospreys, meanwhile, their season goes from miserable to worse. They have now lost all five of their European fixtures to date and 14 of their 15 matches in all competitions.
This game could have been billed as the crisis club derby, given how torrid a season Ospreys and Saracens had endured.
The English and European champions were still picking up the pieces from a deduction of 35 points and £5.36m fine for breaching the salary cap, while Ospreys were in the midst of their worst campaign, without a head coach and in disarray on and off the field.
Saracens' Champions Cup crown sat a little unsteadily having lost two of their first four matches but, with wins in their other two fixtures, they still had hope of qualifying.
However, that aspiration took an early hit in Swansea when Wales loose-head Carre was shown a red card by referee Alexandre Ruiz for a tackle in which his shoulder appeared to connect with the head of Ospreys full-back Evans.
Coincidentally, this was Evans' first game back after a four-week suspension for an even quicker dismissal, just 37 seconds into December's Champions Cup loss to Racing.
Carre's departure - with Wales head coach Wayne Pivac watching in the crowd - was a leveller in what had been expected to be a one-sided affair.
Although Saracens had rested England players such as Owen Farrell, Maro Itoje and Billy Vunipola, their enviable strength in depth meant they were still able to name a team they thought would overpower their opponents.
And despite their numerical disadvantage - made worse when Calum Clark was sin-binned during the first half - they were still fiercely competitive, forcing several turnovers and building a 12-3 lead thanks to Vunipola's penalty kicking.
It was telling that Saracens had responded to Carre's red card by bringing replacement loose-head Richard Barrington on for full-back Elliott Obateyinbo, making his first European start.
Some teams might have feared leaving themselves exposed in the outside back positions, but the champions were willing to take that risk to ensure they were still a force up front.
It was almost as if they were laying down the gauntlet to their confidence-shy opponents: try and beat us out wide if you think you can.
To their credit, Ospreys accepted the challenge and made use of their greater numbers, with fly-half Luke Price stretching the game and supplying the key passes for Evans' tries either side of half-time.
That put the hosts in front, daring to dream of causing a major upset.
But they were soon brought back down to earth as Saracens hit back five minutes later, Lewington catching a high ball before racing clear for a converted score which put his side 19-15 ahead.
Once they were back in front, they never looked like surrendering their lead.
Whereas Saracens never know when they are beaten, Ospreys seem to have forgotten how to win.
Ospreys forwards coach Carl Hogg said: "I think we missed out on a golden opportunity. Saracens went down to 14 men and we had an opportunity to win a game.
"I think our discipline in the first half allowed them to get a foothold and build that lead but I still think we had chances just after half-time, so we're disappointed not to take that opportunity.
"They're one of the best sides in Europe. It's very difficult to chase Saracens when they get in front. So we were architects of our own downfall in that first half."
Saracens director of rugby Mark McCall said: "We were down to 14 men for the whole match and to problem-solve the way players did was outstanding.
"Our senior players - Jackson Wray, Richard Wigglesworth, George Kruis - were magnificent out there and came up with the right answers to the questions that were posed.
"And our younger players listened to what they said and got stuck in. It was a great win."
On Rhys Carre's red card: "I haven't had a close look at it but if the referee says it was head contact, you've got to face the consequences. I haven't seen it close enough."
Ospreys: D Evans; Dirksen, North, Thomas-Wheeler, L Morgan; Price, Venter; Marfo, Otten, Fia, Beard, Alun Wyn Jones, Lydiate (capt), Cross, M Morris.
Replacements: Parry, Fawcett, Gardiner, Ashley, Baker, A Davies, C Evans, Klim.
Saracens: Obatoyinbo; Maitland, Lozowski, Tompkins, Lewington; M Vunipola, Wigglesworth; Carre, Singleton, Lamositele, Skelton, Kruis, Isiekwe, Clark, Wray (capt).
Replacements: Woolstencroft, Barrington, Koch, Kpoku, Reffell, Whiteley, Segun, Crossdale.
Referee: Alexandre Ruiz (France).
Assistants: Ludovic Cayre (France) & Cedric Marchat (France)
TMO: Patrick Dellac (France)
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