The home side gave their own hopes of qualification a boost by opening up a nine-point interval lead after being given first use of a strong breeze at their backs after Saracens won the toss.
The Scarlets were starved of possession for much of the first 40 minutes but did manage to open up a 6-0 lead with penalties for Stephen Jones, who finished up with 21 points, on 10 and 15 minutes for a ruck offence and offside respectively.
That was after Jones missed a penalty attempt from just inside his own half in the third minute. Saracens responded but made little headway as the Scarlets unleashed some aggressive defence.
Saracens did get across the line through hooker Fabio Ongaro but the television match official was unable to give a try. The Scarlets were living too close to the edge of the ruck laws for referee Dave Pearson's liking. Adam Eustace came in from the side of a ruck but Gordon Ross' penalty attempt held up dramatically in the wind.
Pearson's patience with the Scarlets ran out when he sin-binned Simon Easterby for failing to roll away from a ruck. And two minutes later the home side conceded a penalty try from a five-metre scrum, which was converted by Ross to give Saracens a 7-6 lead.
It was a short-lived advantage, however, as the Scarlets, still down to 14 men, launched a try-scoring counter-attack. Dwayne Peel's tap penalty saw Mark Jones make a searing break into the opposition 22 before Eustace put in fellow lock Scott Macleod.
And the Scarlets stretched their lead with a Jones long-range penalty in first-half injury time.
The second half started in frenetic fashion with five tries scored in 16 minutes as both sides went in search of bonus points. Stephen Jones started the scoring sequence, converting his own try after being put over by Peel after a concerted attack by the Scarlets.
But that was cancelled out by Saracens centre Adam Powell who darted over before the home side crossed twice in four minutes to seal a bonus point.First Jon Davies evaded tackles to race in down the right before Garan Evans was put over by Regan King.
That left the Saracens needing to score four tries and gain a losing bonus point. They achieved the first when wing Kameli Ratuvou went in at the left corner and, following a Stephen Jones penalty, Saracens were awarded their second penalty try from a scrum.
Crucially, Farrell kicked a penalty from in front of the posts three minutes from time and then with the last kick of the game made sure of qualification with a second penalty goal. The Scarlets won the match with a bonus point but it was very much a hollow victory.