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Ireland, who lost flyhalf Jonathan Sexton and wing Simon Zebo to injury in a first half in which the host's handling was simply abysmal, trailed 6-0 at the break thanks to the ever-reliable boot of flyhalf Farrell.
England, whose last championship victory in Ireland also coincided with their last Grand Slam win, were pegged back thanks to two penalties from replacement flyhalf Ronan O'Gara, but Farrell restored their six-point lead just after the hour.
Both flyhalves missed a further shot each at goal in the closing minutes as England, who next host a French team already virtually out of the championship following two opening losses, comfortably saw the victory out.