Full-back Jared Payne's fifth-minute dismissal for an adjudged dangerous tackle on Alex Goode called the tune for the remainder of the match, with Saracens reaping three tries through expertly exploiting their numerical advantage.
The Ulstermen kept in touch thanks to consistent kicking from Ruan Pienaar and Paddy Jackson, but it was not enough in a gripping finish.
Ulster fall, therefore, at the same hurdle as they did in last year’s tournament - and to the same opposition - after a bruising battle which saw three first choice players - Pienaar, Rory Best and Andrew Trimble - make early exits due to injury.
The Ulster starting line-up was arguably Mark Anscombe's strongest possible team, with Best returning at hooker and Pienaar back at scrum half after a three-week lay-off with a shoulder injury.
The main area where personnel may have been open to deliberation - the back row - saw Roger Wilson, Chris Henry and Nick Williams line up together.
Meanwhile, Iain Henderson, Robbie Diack and Stephen Ferris - back from a year-and-a-half's injury hiatus but yet to complete a full 80 minutes - all looked to make an impact from the bench.
An early penalty miss from Owen Farrell was quickly followed by an aerial collision between Payne and his opposite number Goode as the England international leapt to collect Jackson’s up-and-under.
The challenge left the Saracens full-back prostrate for a good five minutes, and eventually saw Payne red carded by referee Jérôme Garcès after advice from television match official Eric Gauzins.
With Goode stretchered off and replaced by Chris Wyles, and Tommy Bowe covering the Ulster full-back berth, Saracens attempted to put the squeeze on straight from the restart.
The province dug in and Bowe and Jackson almost powered through the spine of the visitors' midfield on 10 minutes in a speedy breakaway.
Best limped off to make way for Rob Herring a few moments later, but Pienaar's 15th-minute penalty from the 10-metre line soon settled Ulster nerves after the most frenetic of starts.
The Springbok narrowly missed out on adding a second from a similar distance three minutes later, and Saracens were soon on the scoresheet.
Mark McCall's charges spotted some space off the side of a scrum, springing the tournament's top try scorer Chris Ashton through a gap and his angled run led to him diving over in the right corner.
The damage was limited as Farrell's conversion kick veered wide, and a neat intercept by Bowe as Saracens threatened again got Ulster to the brink of their opponents 22.
The hosts' ferocious mauling forced an infringement that allowed Pienaar to kick his side back into the lead.
With Richard Wigglesworth knocking a 33rd minute penalty to touch, the Premiership side put together a strong maul of their own, threatening down the right flank until the attack was broken up by Ulster persistence and Pienaar cleared.
The South African, involved in everything Ulster did well, only just missed with a penalty attempt from well inside his own half in the 36th minute.
But he did send the province into the dressing rooms 9-5 to the good with an expertly-struck kick from wide on the left.
Despite their numerical disadvantage, Ulster - roared on by a very vocal capacity crowd - came out for the second half very much on the front foot.
Anscombe's charges bossed several early lineouts and their half-back partnership kicked judiciously and accurately.
However, Saracens' superiority shone through on 48 minutes as Moritz Botha crossed the whitewash after patient approach play across the Ulster five-metre line from left to right.
Farrell's lack of accuracy once again spared Ulster further punishment as his conversion spiralled wide, but worse was to follow for Ulster as Pienaar succumbed to injury and Jackson hit a 53rd minute penalty against the upright.
Paul Marshall came on at scrum half, joined by Ferris and Henderson, and as the match hung in the balance on the hour mark, Farrell once again fluffed his lines, this time from a central position 25 metres from goal.
Trimble was next to leave the pitch, injuring himself in a try-saving tackle on man-of-the-match Billy Vunipola. The Ireland winger was replaced by fellow international Craig Gilroy.
Ashton then delivered the killer blow, completing his brace on 66 minutes as he collected Farrell’s pinpoint cross-field kick near the right corner flag, with the out-half this time making his conversion count.
Two penalties in quick succession from Jackson reduced the gap to two points just after the 70-minute mark, and another poor kick from Farrell - this time a clearance which bobbled behind the Ulster line - gifted Ulster the scrum in the middle of the pitch.
Led superbly once more by Johann Muller, the hosts launched into their last blast, recycling time after time on Sarries' 10-metre line.
Ultimately, their heroic efforts were in vain as the English side eventually drew the infringement which booked their place in the semi-finals where they will host Clermont Auvergne at Twickenham.
Ulster must now focus on the remainder of their RaboDirect PRO12 campaign and securing a play-off berth, starting with next Friday's home derby match against Connacht.