The Ospreys gave everything at the home of the three-time European champions, but it was not enough as Saracens claimed a 35-20 triumph at StoneX Stadium.
Toby Booth’s men were excellent in the first half and had the hosts under significant pressure, taking a 14-3 lead through Michael Collins and Keiran Williams tries.
Sarries were struggling to find their rhythm, but after Owen Farrell kicked a second three-pointer, Max Malins went over to reduce the arrears to one point at the break.
Successive Owen Williams penalties in the second period once again extended that buffer, but from that point onwards, the home side dominated.
Malins’ second try levelled matters before Farrell took Saracens ahead with just under a quarter of the match remaining.
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The Ospreys still had a chance, but Rhys Webb’s awful error, when his quick lineout was intercepted by Duncan Taylor, effectively sealed their fate. Tom Woolstencroft’s try then rubberstamped the victory as Sarries secured a game with holders La Rochelle in the Champions Cup quarter-finals.
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League form pointed to a comfortable home win with Saracens leading the Premiership and Ospreys sat 12th in the United Rugby Championship, but the only Welsh side left in the knockout phase instead went toe-to-toe in a pulsating clash.
They lost wing George North shortly before kick-off but still paraded nine internationals, and it was not until Malins claimed the second of his two tries in the 57th minute that Saracens were back in the hunt.
It was a far-from-vintage display from the three-time European champions, but they had the resilience to set up a last appointment with La Rochelle next weekend, becoming the third English club behind Leicester and Exeter to reach that stage.
Woolstencroft’s late try distorted the final scoreline, which, from an early stage, seemed beyond Mark McCall’s men.
A Farrell penalty rewarded Saracens’ early dominance, but two tackle-busting carries by centre Williams punched holes in their defence, with full-back Collins crossing to round off the second.
Having seen their try-line breached, the hosts stepped up a gear with a driving maul held up over the line before quick ruck speed and hard running created a chance on the left with only the killer instinct missing.
But in classic rope-a-dope fashion, the Ospreys soaked up the pressure and then pounced on a mistake, Webb grabbing the ball as it squirted out of Nick Tompkins’ hands and launching a move that ended with Keiran Williams touching down.
Nicky Smith and Justin Tipuric were also involved in a superb try, and shortly after, only robust defence prevented Saracens’ line from cracking a third time.
Three points from Farrell rounded off a brief siege on the visitors’ whitewash, and another key moment arrived when the excellent Keiran Williams was shown a yellow card for killing the ball as he halted a dynamic break by Ben Earl.
Malins crossed in first-half overtime to continue the momentum shift, although it was uncertain whether he had properly grounded the ball.
Owen Williams rifled over a penalty to open a four-point lead for the Ospreys, and the contrasting fortunes of the Vunipola brothers were on full display as Billy knocked on twice while Mako made two impactful charges downfield.
Smith continued the theme of props making bullocking runs into space, but the attack ran out of steam and in the 57th minute, Saracens found their ruthless streak as Alex Goode chipped ahead for Andy Christie to send Malins over.
For the first time since the 10th minute, Saracens took the lead through a Farrell penalty, and when Taylor punished Webb’s moment of madness, it was all over.