Saracens (6) 19
Try: Leonelli Con: Jackson Pens: Jackson 3 Drop: Jackson
Ospreys (3) 10
Try: James Con: Hook Pen: Hook
The quarter-final win is a landmark achievement for Saracens
Saracens claimed a place in the semi-finals of the Heineken Cup for the first time after stunning favourites Ospreys at Vicarage Road.
James Hook put the visitors ahead with an early penalty but Saracens hit back with two penalties from Glen Jackson.
The Ospreys made a host of errors and Saracens took control with a try from Francisco Leonelli on 42 minutes.
Ospreys had a glimmer of hope after Paul James bundled over but Jackson's late drop-goal sealed a famous win.
Saracens can now look forward to a Heineken Cup semi-final against Munster at the Ricoh Arena in Coventry after a victory which will be sweet revenge for the 30-3 defeat they suffered at the hands of the Ospreys in the EDF Energy Cup last month.
The Welsh region, boasting a dozen players who won the Six Nations with Wales this year, made the better start - fly-half James Hook slotting over a penalty after just three minutes.
But Saracens, playing in front of a sold-out Vicarage Road for the first time, came back into the game helped by a raft of penalties given against the visitors.
Jackson put his side level with 10 minutes gone before adding another three points after Marty Holah was penalised for hands in the ruck as Saracens pressurised the Ospreys line.
The Ospreys thought they had scored the game's first try when the ball bounced into the in-goal area but Alun Wyn Jones was adjudged to have tackled Neil de Kock without the ball before he touched down.
The contest stated to open up as the penalty count dropped and both sides began to carve out chances only for poor execution to let them down.
Impressive Sarries wing Richard Haughton made a darting run through the Ospreys defence from deep only to deliver a poor pass at the crucial moment while Sonny Parker and Lee Byrne both spilled the ball as the visitors launched dangerous-looking attacks.
Saracens lost centre Andy Farrell and full-back Brent Russell before the break but it did not seem to affect them as they were almost handed a try following a moment of madness from Hook.
The mercurial number 10 tried to catch a high ball in the 22 behind his back but dropped it and then sliced his clearance into touch.
From the resulting line-out, Haughton again made a searing break which led to Paul Gustard just being held up short of the line by the desperate defence of Byrne and Shane Williams.
The Ospreys struggled to cope with Saracens' aggressive defence
A score for the home side was not long in coming though and they crossed two minutes after the restart thanks to an enormous slice of luck from de Kock's deep clearance.
The kick was touched in flight by Holah, allowing Saracens to collect the loose ball which led to Leonelli, who had came on for Russell, to touch down in the corner.
The Ospreys seemed rattled by the score and a combination of mistakes and ferocious Saracens defence meant they struggled to find any momentum.
Saracens continued to carve out chances and lock Hugh Vyvyan was bundled over the line only for the television match official to rule that he had been held up.
The Ospreys cause was not helped by the sin-binning of Byrne on 58 minutes, who saw yellow for a deliberate knock-on as Jackson burst through the defence and passed the ball wide.
With the game entering the final 10 minutes, the Ospreys battered the Saracens line and the brave defence was finally broken when James crashed over from close range.
There was to be no fairytale comeback however and Jackson's drop-goal with two minutes left completed the victory, handing coach Alan Gaffney the chance to try and overcome his former club Munster in the last four.
Saracens: Russell; Haughton, Sorrell, Farrell, Ratuvou; Jackson, De Kock (capt); Lloyd, Cairns, Visagie, Vyvyan, Chesney, Gustard, Hill, Skirving.
Replacements: Ongaro, Johnston, Ryder, Barrell, Rauluni, Powell, Leonelli.
Ospreys: Byrne; Vaughton, Parker, Henson, Shane Williams, Hook, Marshall; Duncan Jones, Bennett, Adam Jones, Gough, Wyn Jones, Jonathan Thomas, Holah, Ryan Jones (capt).
Replacements: Hibbard, James, Ian Evans, Tiatia, Webb, Bishop, Brew.
Referee: Alan Lewis (Ireland).