Saracens boss Mark McCall insisted his Heineken Champions Cup title hopefuls had risen to the occasion after being threatened with an upset by the Ospreys.
The Gallagher Premiership leaders needed a late Duncan Taylor try to pull clear in a 35-20 victory at StoneX Stadium that set-up a quarter-final against champions La Rochelle, who crept past unfancied Gloucester on Saturday.
It came as part of a salvo of 22 unanswered points, having trailed for 52 minutes as the Ospreys showed the killer instinct in attack lacked by the hosts until Max Malins plundered two tries.
"We had a proper test and we passed it. We didn't play as well as we'd have liked for the first 55 minutes," McCall said.
"I'm really pleased about that last 25 minutes against a good side. Everything was different - more aggressive and proactive.
"There was a different intensity about us. In the first 55 minutes we looked like a team that had a lot to lose.
"In these games against good teams like the Ospreys, everything just doesn't go your way.
"You have to dig in and go through some tough moments and tough periods. We ended up enjoying that test and relished the battle.
"There will be another battle next weekend, which is very exciting because we've never been to La Rochelle before and they're the reigning champions. Gloucester might have poked the bear a little bit."
Taylor delivered the decisive blow in the 69th minute when he ran on to a quickly taken throw-in by Rhys Webb to touch down, punishing a terrible blunder by the Wales scrum-half.
"To be that alive and that switched on and to see it happening before anyone else saw it happening was superb. That was one of the best first touches," McCall said.
The victory has come at the cost of injuries to Andy Christie and Alec Clarey, however, with the forwards suffering a suspected broken arm and suspected broken wrist respectively.
Webb admitted his fault for Taylor's try, but Ospreys boss Toby Booth refused to blame his half-back.
"It was just on me," Webb said. "I thought he put his hand up to call for it. Instinct. It is what it is."
Booth added: "When you play Saracens, you have to take them out of their rhythm. You have to force a bit.
"We knew we would have to do it our way. A lot of those things worked well for us. In that instance, it didn't. But we have no regrets."
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