Irish took the lead through a Tom Homer kick but Farrell struck three times before the break to hand the Aviva Premiership champions the advantage at Vicarage Road.
Daniel Bowden's penalty reduced the deficit before two more Farrell kicks made it 15-6. David Paice secured the Exiles a losing bonus point with the only try of the match, which Bowden failed to convert.
The match got off to a bad start for the hosts with wing Joe Maddock lost to a leg injury after just three minutes, David Strettle his replacement off the bench.
Homer fired Irish into the lead on five minutes with a penalty which Farrell cancelled out three minutes later.
Irish had the chance to regain the lead after lock Matt Garvey smashed through three tackles before being hauled down. Saracens then had hooker John Smit sin-binned for picking up the ball after it had emerged from the back of the resulting ruck, but Homer fired his subsequent penalty attempt wide.
This miss was a costly one, with Saracens taking the lead on 15 minutes courtesy of Farrell's second goal, before the 20-year-old added his third kick of the half when Irish were caught offside on 22 minutes.
Irish responded by laying siege to the hosts' line, winning a succession of scrums, but the Saracens defence stood firm.
The best chance for either side to bag a try in the opening period went to the hosts on the stroke of half-time, James Short going over after collecting Farrell's chip only for the video referee to rule he had failed to ground the ball under pressure from Bowden.
Irish went back on the offensive from the re-start with the impressive Garvey and Chris Hala'ufia again a threat with their powerful ball-carrying.
Irish were rewarded for their perseverance when Bowden drove a 49th-minute penalty between the posts.
Yet within minutes Irish were penalised for not releasing after Matt Stevens had won a scrum and set up an attack on the right, Farrell's 52nd-minute penalty restoring Saracens' six-point lead.
And Farrell made it five from five on 69 minutes, a 40-metre effort that left Irish requiring two scores to win.
They got the first on 76 minutes, the pack driving for the line and propelling Paice over for a try which Bowden failed to convert, but that was the end of the scoring.
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