Ashton, who suffered a major form lapse during this season's Six Nations Championship, touched down 17 minutes from time to confirm a Twickenham last-four appointment with Toulon or Leicester on April 28.
England fly-half Owen Farrell kicked 17 points from five penalties and a conversion of flanker Will Fraser's first-half try as a crowd of just under 38,000 saw Saracens never seriously troubled.
Ulster had fleeting moments but they failed to consistently trouble Saracens defensively after the home team took control from an early stage.
Scrum-half Ruan Pienaar booted three penalties for Ulster and converted flanker Iain Henderson's late try, yet they never threatened a repeat of last season's Heineken Cup heroics that saw them reach the final.
Saracens, five points clear at the Premiership summit, looked a team in control throughout and Ulster had no answer at the crucial moments as Saracens' try-line did not look like remotely being breached.
Ulster plugged away in search of a consolation score but Saracens were having none of it, and they comfortably preserved an 18-point margin that accurately reflected their dominance.
Saracens, aiming for a domestic and European double this season, fielded their clutch of current England stars under Steve Borthwick's captaincy while Scotland skipper Kelly Brown was also among those looking to impress British and Irish Lions coach Warren Gatland.
Another Lions hopeful - Ireland wing Tommy Bowe - featured on the Ulster bench for his first matchday involvement since suffering a knee injury four months ago as last season's beaten Heineken finalists returned to the scene of that 42-14 defeat against Leinster.
Farrell booted Saracens ahead through a second-minute penalty but the opening exchanges were dominated by largely aimless tactical kicking from both teams as try-scoring opportunities proved few and far between.
Ulster quickly grew into the game but Pienaar missed two penalty chances in three minutes - his second attempt hit the post - but he made no mistake from close range two minutes later.
And with Saracens finding themselves under increased scrummage pressure, England prop Mako Vunipola was penalised after being demolished by Ulster tighthead John Afoa and Pienaar hauled Ulster level.
They were only on level terms for three minutes, though, as a concerted spell of Saracens pressure resulted in Fraser powering over, although it required several reviews by television match official Eric Gauzins before the try was awarded.
Farrell converted and then kicked a penalty as half-time approached, hoisting Saracens 10 points clear to give them a degree of breathing space for the first time.
And when Farrell added a further penalty eight minutes into the second period Ulster had a mountain to climb, trailing by 13 points and with seemingly little hope of replicating last season's achievement in Europe.
Ulster tried to increase the tempo but Saracens were not noticeably threatened defensively despite some powerful Ulster surges led by blindside flanker Iain Henderson.
Farrell kicked another penalty to give Ulster further cause for concern and victory was sealed when prop Rhys Gill secured possession in midfield and Ashton ran around two defenders to claim a try that he celebrated with a trademark dive.
Bowe featured off the bench late on but Ulster were already down and out, well beaten by a team whose superior organisation and collective excellence made it a one-sided affair.
Henderson had the final say, posting a try that Pienaar converted, but it was Saracens' day and they now await the outcome of events in southern France on Sunday.