Farrell showed just the kind of composure that has seen him earmarked for Test honours since the age of 14 to land his fifth penalty three minutes from time to seal the win.
Saracens had led 14-6 at the interval courtesy of a try from scrum-half Ben Spencer and Farrell's first three penalties before Biarritz came back at them in the second half.
Dimitri Yachvili scored all of the points for Biarritz, including a charge-down try, as the French visitors pushed Saracens to the wire and earn a losing bonus point.
But Saracens now need only gain a single point against Treviso next weekend to confirm their place in the last eight.
Saracens had wanted to break new ground by taking this fixture to South Africa but a local row over which Cape Town stadium was to be used eventually scuppered the idea.
Vicarage Road is certainly no Newlands. The three-sided stadium is in the shadow not of Table Mountain but of Watford General Hospital.
But Saracens certainly looked as if they had benefited from their week's warm-weather training in Cape Town as they hit Biarritz with a ferocious forwards performance and some dazzling back play.
The French visitors twice took the lead with penalties from Yachvili, either side of a strike from Farrell, before Saracens capitalised on a mistake to score the opening try.
Yachvili tried to force a pass in midfield but the ball went to ground and Saracens counter-attacked through David Strettle, Ernst Joubert and Chris Wyles.
The American wing was halted but Spencer darted from the base of the ruck, deftly evading three tackles before diving over to push Saracens into the lead.
Farrell missed with the touchline conversion but Saracens, with their pack on top and their potential England midfield of Charlie Hodgson, Brad Barritt and Farrell to the fore, kept Biarritz under pressure.
Alex Goode threatened from full-back with one break before lock Mouritz Botha, another member of England's Six Nations plans, picked off an interception and charged downfield.
Strettle cut in off his wing and almost broke clear but Biarritz were penalised for being offside at the ruck and Farrell extended Saracens' lead.
The Saracens pack, with John Smit at hooker and Carlos Nieto preferred on the tight-head, were on top and won a penalty on half-way that Farrell converted to secure a 14-6 lead at the interval.
The temperature rose in the early exchanges of the second half as Biarritz threatened, working a platform for Marcelo Bosch to attempt a drop-goal which drifted just wide.
Saracens' quick line speed was making life difficult for Biarritz but on the back of an improving kicking game they worked their way back downfield.
Goode collected a high ball outside his 22 but he was quickly swallowed up and Peter Stringer, who had been sent on for Spencer, saw his box kick charged down by Yachvili.
The Biarritz scrum-half followed up and muscled his way ahead of Goode to touch down and then convert to bring his side back to within a single point.
Farrell eased Saracens' nerves with his fourth penalty but only briefly, with Yachvili responding in kind after Smit's high tackle on Biarritz hooker Arnaud Hegny.
But with three minutes remaining the Saracens centre, called into England's Six Nations squad this week, drilled his fifth penalty to seal a tight victory.
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