The star-studded Welsh region were made to scrap every inch of the way by a fired-up London Irish side that led 20-6 just after half-time.
There appeared no way back for the Ospreys after centre Sailala Mapusua and wing Sailosi Tagicakibau – they will both be on Pacific Islands duty against England at Twickenham next weekend – scored tries.
But fly-half James Hook’s precision goalkicking – he booted 14 points – and wing Nikki Walker’s 54th-minute touchdown kept Ospreys in contention.
Irish dominated territory and possession for large parts of a stirring Madejski Stadium encounter, yet victory was still not enough to end Ospreys’ reign as Anglo-Welsh cup kings.
Home full-back Peter Hewat kicked 13 points, but despite Ospreys hanging on for dear life during the closing seconds, Irish could not administer a telling blow.
The Ospreys included six members of Wales’ autumn Test squad in their starting line-up, with five more among the replacements, but full-back Lee Byrne and lock Ian Evans were both rested.
Irish, fully aware they still had a semi-final chance, paraded 11 internationals and had no intention of playing second fiddle to the cup holders.
Hook booted the Ospreys into a 6-0 lead inside 20 minutes, but Irish had already built an imposing territorial platform – and they prospered with devastating effect.
The Ospreys’ defence was repeatedly pummelled, and Irish finally broke through nine minutes before half-time.
Aggressive approach work by the Irish pack, with flanker Steffon Armitage and skipper Bob Casey in the driving seat, eventually took its toll.
And Mapusua was the recipient of Shane Geraghty’s pass, crashing over near the posts for a try that Hewat converted.
But the Ospreys’ problems deepened just three minutes later – and this time they only had themselves to blame.
Gavin Henson, who was anonymous for the opening 30 minutes despite his orange shirt and yellow boots, threw a reckless pass to midfield partner Tommy Bowe on halfway, and Irish made him pay.
Possession came back on the Irish side, and Tagicakibau did not require a second invitation to skip around opposite number Walker before setting off on an unopposed 50-metre sprint.
Hewat added the extras, following an earlier penalty, hoisting Irish 17-6 clear as Ospreys full-back Jonny Vaughton departed injured on the stroke of half-time and was replaced by Andrew Bishop.
Hewat and Hook exchanged penalties early in the second period, and although the Ospreys had no reason to panic, there was sufficient alarm for coach Sean Holley to make a notable double 52nd-minute substitution.
Forwards Ryan Jones and Alun-Wyn Jones, who will both start for Wales against world champions South Africa next Saturday, entered the fray, and there was an immediate urgency about Ospreys’ play.
Barely 100 seconds after the reinforcements arrived, Ospreys struck, as Bishop’s weaving run caused panic in the Irish defence and Walker finished off a crisp move.
Hook converted, cutting Ospreys’ deficit to just four points, but there was also an injury scare for the visitors – and Wales coach Warren Gatland – as hooker Huw Bennett limped off.
The Ospreys had clawed their way back impressively, yet another Hewat penalty – his third – made it 23-16 entering the closing quarter, as Irish player-coach Mike Catt replaced Geraghty.
If the Ospreys were not going to win, they knew it was a case of remaining within losing bonus point range.
And Hook certainly played his part, booting a magnificent 52-metre penalty that meant Irish’s lead was back to four points with little more than 10 minutes left.
The finale proved an inevitably tense business, with errors creeping in on both sides, but the Ospreys held on to book a semi-final place at Coventry’s Ricoh Arena next March.
