Alex Goode fired leaders Saracens to a sixth successive Premiership victory as his penalty with the game's final kick edged out Exeter.
Chiefs centre Henry Slade looked to have responded to his omission from England's autumn squad by kicking a decisive penalty four minutes from time.
But Goode, on as a replacement for Farrell and making a record-equalling 338th Saracens first team appearance, came up trumps with the clock in the red to seal a 22-20 success.
Owen Farrell and England colleague Mako Vunipola were earlier yellow carded, with Vunipola - playing his first game after a three-match ban - being sin-binned for collapsing an Exeter driving maul and conceding a penalty try in the process.
But Saracens largely kept their composure on a testing afternoon as flanker Theo McFarland scored a first-half try, while Farrell converted and kicked two penalties, with full-back Elliot Daly adding two long-range strikes and Goode a late clincher.
Exeter had their moments, but not enough of them, to disrupt Saracens' well-oiled machine, ensuring a tense finish after number eight Jacques Vermeuelen's 71st-minute try that centre Slade converted, following an early penalty and the penalty try.
Saracen's director of rugby Mark McCall said: "It was two really good sides scrapping it out, fighting it out. Whether we deserved to win I am not sure, but we showed some great fighting qualities.
"We were down to 14 men twice and I liked how we went about that and how physical we were. I don't think we were as good as we should have been in the second-half."
On Goode's match-winner, McCall added: "I think it might have been his first kick of the season. It tells you a lot about Alex Goode that he was prepared to take the responsibility on his shoulders."
It was Exeter's second Premiership defeat of the season and they are 14 points behind pace-setters Saracens.
But head coach Ali Hepher said: "We were in the fight. These games come down to tight margins and we've got to get more clinical.
"We are in the right space mentally and we've everything to work with. We came up a little bit short today."
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