With two games remaining in the pool stage, Saracens hold a two-point advantage over Racing Metro at the top of Pool One and a three-point cushion over Munster who now have it all to do to remain in the competition.
Saracens were deserved winners at Vicarage Road, overcoming the loss of Will Fraser to the sin bin, but had to rely on 14 points from the boot of Farrell for their success.
Munster grabbed an interception try from Doug Howlett but failed to take advantage of Fraser's absence and two late misses from Ronan O'Gara cost them dearly.
The game began with a spark as the first ruck culminated in a heated melee between the packs, resulting in a warning being given to the captains.
The opening minutes were frenetic as both sides harried each other into mistakes. Saracens had the first sustained attack and the first scoring chance but Farrell's 25-metre drop-goal attempt sailed narrowly wide.
After eight minutes, Farrell was given another opportunity and this time he was on target with a long-range penalty.
A poor kick from Farrell, which went straight to Simon Zebo, gave Munster their first chance to counter-attack. O'Gara produced an exquisite chip over the top for Zebo to collect but a knock-on by hooker Mike Sherry prevented the move from developing.
Saracens conceded a penalty at the resulting scrum but O'Gara fired wide, however moments later the outside-half made no mistake with his second effort after Farrell had been penalised for not releasing.
Munster suffered a setback when full-back Felix Jones limped off, to be replaced by Luke O'Dea, but although Saracens had marginally the better of the first quarter it was still 3-3 at the end of it.
However after 22 minutes, the hosts scored the opening try when Farrell's clever chip through saw David Strettle easily win the race for the touchdown which Farrell converted.
Back came Munster to tie up the scores. Farrell's loose pass on half-way was intercepted by James Downey, and although the centre was caught by Strettle he got the ball away to Howlett who scored for O'Gara to convert.
Saracens continued to dominate in terms of possession and territory but they could not make it count at that stage.
Strettle was hauled down just short of the line and Farrell missed a penalty so it remained at 10-10 at the interval.
When O'Dea fumbled an up-an-under early in the second half, it allowed Saracens a position in the visitors 22. Munster were penalised but again Farrell could not take advantage.
Against the run of play, O'Gara put his aside ahead with a penalty after Downey nailed his former Northampton colleague Chris Ashton, who was penalised for not releasing.
Farrell responded with a simple penalty after Munster offended at a scrum and minutes later kicked another to give Saracens a 16-13 lead going into the final quarter.
Saracens suffered a huge blow when Will Fraser was yellow-carded for a high tackle on Howlett.
Munster immediately piled on the pressure for their best period of the match but O'Gara's drop goal and penalty attempts both missed the target.
Saracens survived the onslaught and it was left to Farrell to seal a crucial victory with a penalty four minutes from time.
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