Sarries looked set to suffer a first defeat in Pool 3 when they trailed by seven points at Parc y Scarlets with the clock having ticked past 80 minutes and Will Skelton in the sin bin.
However, England playmaker Farrell then dummied his way through the home backline and passed inside for Chris Ashton to go over by the posts, before adding the extras to the winger's second try.
With one round of fixtures remaining, Saracens are five points clear of Toulon and would be guaranteed a place in the quarter-finals as one of the best runners-up even if they were surprisingly overhauled by the French side - their opponents at Allianz Park next weekend.
That's why @Saracens is a champion team under pressure they still put point on the scoreboard. Well done good game.
— Bakkies Botha (@BakkiesBotha4) January 15, 2017
Toulon's fate remains in their own hands after they scored two tries in the final four minutes against Sale Sharks to seal a 27-12 win and an unlikely bonus point.
Winless Sale were only three points behind when replacement prop Kieran Longbottom was yellow-carded late on - handing Toulon a numerical advantage they ruthlessly capitalised on through scores from Jonathan Pelissie and Josua Tuisova.
Clermont Auvergne secured top spot in Pool 5 with a hard-fought 9-6 win at Bordeaux-Begles, three Camille Lopez penalties proving enough for a visiting side that had two players yellow-carded early on.
Ulster's hopes of qualifying from the same group ended courtesy of a 31-19 loss at Exeter Chiefs, who retain a slim chance of making the quarter-finals.
The outstanding Charles Piutau scored two tries for Ulster in an entertaining encounter at Sandy Park, but both Thomas Waldrom and Michele Campagnaro did likewise to help Exeter leapfrog their opponents and Bordeaux.