Ireland had beaten England in seven of their last eight meetings but failed to adapt to the wet conditions, an epidemic of handling errors costing them any chance of another Twickenham win.
On a day when Wales secured their third Grand Slam in eight years a few hours earlier, the comprehensive manner of England's win - making it four from five - meant Lancaster's job application for the permanent coach's role becomes even more persuasive.
England had the lead within two minutes of the start, Farrell drilling over a penalty after Ireland's scrum had been penalised at the first set-piece.
Steady drizzle made handling difficult with both Jamie Heaslip and Mouritz Botha spilling promising possession, and after Keith Earls accelerated down the right wing Lee Dickson slipped in pursuit of the kick through and came close to conceding a dramatic try.
Full-back Rob Kearney hit the right-hand post with an audacious long-range drop-goal attempt in a frenetic opening, and Ireland were level soon after as Sexton's simple penalty punished Brad Barritt for going offside.
If England struggled occasionally at the line-out their scrum was enjoying some dominance, Eoin Reddan going offside to gift Farrell the chance to make it 6-3 with just over a quarter of the match gone.
Ben Youngs secures England triumph
Tom Croft and Manu Tuliagi both dropped garryowens as the quality dropped away before a trademark rampaging run from Ben Morgan put the Irish under more pressure, but England failed to capitalise and were turned over.
The mistakes kept coming and the atmosphere, spicy at the start, ebbed away. It took Farrell's third successful penalty in three after Ireland skipper Rory Best hacked clear from an offside position to rouse the capacity crowd, and a desperate covering tackle from Chris Ashton to haul down Tommy Bowe after another steepling kick ricocheted from Ben Foden's fingertips.
England dithered in their own 22 on the stroke of half-time, Donnacha Ryan smashing into a ruck to allow Sexton to make it 9-6 at the interval.
The errors continued as battle was rejoined. Dickson knocked on after a scrum won against the head and then Ireland did the same.
Official match stats
Minutes in possession
Scrums won (lost)
Line-outs won (lost)
Tackles made (missed)
(delivered by Accenture)
A wonderful piece of counter-attacking from Foden then almost brought the first try. The full-back went on a curving, accelerating run and set Croft free on a barnstorming burst that seemed certain to replicate his match-winning score against France a week ago, only for the ball to pop from his grasp with the line closing in and Ashton on his inside shoulder.
Ireland's respite was brief. Once again their scrum was mangled and Farrell landed his fourth penalty to extend his side's lead to 12-6.
Next man in an ever-lengthening list to spill the bar of soap was the otherwise outstanding Morgan, and as Ireland counter-attacked Sexton reduced the deficit to three with a penalty after another ruck infringement.
A clever grubber through from Farrell gave England a five-metre scrum and once again they took the men in green apart.
Ben Morgan praises coaching team
Referee Nigel Owens went to his TMO as replacement Tom Palmer dived on the ball as it came loose, awarded another penalty and then, with the England pack in total control, signalled for a penalty try as Twickenham celebrated.
Farrell converted for 19-9, his front row of Dan Cole, Dylan Hartley and Alex Corbisiero bear-hugging behind him.
The demolition job continued. At the next set piece the Irish pack went backwards at pace, Owens blew again and Farrell popped over his fifth penalty to put England 13 points clear with 15 minutes left on the clock.
Youngs spotted a gap in the tired defence after another scrum penalty to take a quick tap and dart over, and Farrell drilled over his sixth penalty with the seconds running out to seal a thumping win.
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