The victory means Saracens exacted revenge over the only side to beat the current champions at home in the Aviva Premiership last season.
England Under-20 fly-half Farrell, the 20-year-old son of former dual Union and League international Andy Farrell scored a try, created two more and kicked 23 points with four conversions and five penalties as the hosts won this LV= Cup contest.
Farrell's pinpoint kicks into the corner also set up Saracens' first two tries after they twice opted to kick for position, rather than go for goal.
Centre Adam Powell, winger Joe Maddock and replacement lock Hugh Vyvyan scored the other Sarries' tries.
Exeter replied with tries from lock Chris Bentley and full-back Myles Dorrian. Fly-half Gareth Steenson kicked their other 10 points. Farrell and Steenson both missed early penalties in the swirling wind.
Then, when Exeter were caught offside, Sarries rejected the goalkicking opportunity, with Farrell finding touch in the corner.
Scotland flanker Kelly Brown, making his first appearance since returning from the World Cup, took the lineout cleanly, Farrell judged his through kick to perfection and Powell won the race to touch down behind the posts in the 16th minute, leaving Farrell an easy conversion.
Richard Wigglesworth, another World Cup returnee, fared less well.
The England scrum-half's homecoming ended after only 20 minutes when he was replaced by Ben Spencer.
Exeter drew level in the 24th minute after Steenson's wind-assisted penalty found touch deep in the Saracens half.
Their lineout produced an effective rolling maul and, after Sarries transgressed by pulling it down, a quick tap penalty sent lock Bentley in for his try, with Steenson converting.
Some of the tackling was fierce and Saracens also lost No 8 Jackson Wray, replaced by debutant Matt Hankin, in the first half.
Farrell and Steenson exchanged penalties to keep the scores level at 10-10 before Sarries were, for the second time, rewarded for their enterprise after again spurning the chance to kick for goal.
Farrell again found touch in the corner and, Winning the lineout, the home side quickly switched the play from left to right.
The young fly-half's long pass to Joe Maddock stretched the Exeter defence, the full-back found winger Penney, making his 102nd appearance for the club, and raced over in the left-hand corner after 35 minutes.
Farrell landed the difficult conversion to send Sarries in 17-10 ahead at half-time.
Steenson reduced the deficit to four points with his second penalty three minutes into the second half.
But, as Saracens took a grip on the game, Farrell responded with four more of his own - the last one from inside his own half - to increase the home side's lead to 16 points.
Exeter introduced Samoan scrum-half Junior Poluleuligaga off the bench for the first time since his return from the World Cup but he was unable to stop a Saracens side in full flew.
Replacement full-back Alex Goode had a big part in Saracens' final two tries.
His high kicked bounced well for Farrell to collect and score his team's third try, before a length-of-the-field attack ended with Goode providing the final pass for Vyvyan's try - both converted by Farrell.
Exeter's perseverance produced a late consolation try for full-back Myles Dorrian, converted by Steenson.
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