Ian Humphreys's penalty helped Irish to reduce the deficit, but Farrell added another three points with the boot to push his side further ahead.
Saracens looked to turn the screw in the final five minutes of the first half thanks to a second try from George, only for Kieran Low to touch down moments later before Humphreys added the extras.
However, Farrell had the final say of the opening period as he kicked over his third penalty of the afternoon to give Sarries a 21-10 advantage.
A pair of penalties from Farrell at the start of the second half made it 27-10 before Humphreys kept Irish's slim hopes alive with another kick between the posts.
Mako Vunipola's try on 65 minutes, converted by Farrell, then saw the away side pull clear.
Marland Yarde went over with 10 minutes left as Irish continued to battle away, though it was ultimately in vain as a final Farrell penalty and a late try from Ashton sealed the bonus-point win for Saracens.