Having struggled for much of Farrell's 13-month tenure, Ireland survived some early pressure before a brilliant lineout move ended with Keith Earls touching down and a deserved second try by Jack Conan gave the hosts a 20-6 halftime lead.
Buffered by Johnny Sexton's boot, Ireland remained in total control and not even a red card for centre Bundee Aki and tries for Ben Youngs and Jonny May threatened an uncomfortable finale as the defending champions were pummelled into submission.
"It shows the highs we can hit when we're on and where we can go in the future," man of the match Robbie Henshaw said in a pitchside interview after Ireland's first win over England in five games injected some momentum into the Farrell era.
With the retiring CJ Stander in tears on the pitch at the final whistle, Ireland looked set for a top-three finish while England ended with more defeats than victories for only the second time in 15 years and set for a disappointing fifth spot.
It was also the first time since 1976 that England had lost in the championship to Ireland, Scotland and Wales, the nations that compete each year for the Triple Crown.
"As disappointed as I am about the result, we still know where we're going," coach Eddie Jones told a news conference.
"The main thing we're missing at the moment is consistency of performance. That sometimes happens to a team but we'll get that back."
BRILLIANT HENSHAW
While England's early superiority forced the hosts into conceding four penalties in the first 10 minutes, they had only an Owen Farrell penalty to show for it before Sexton levelled it up with Ireland's first foray in the opposition half.
Ireland's defence, permeated by absent minded moments in last week's narrow victory over Scotland, was far better, led by the brilliant Henshaw, who almost single-handedly swung the penalty count back Ireland's way.
They would only concede five more penalties to England's 14.
Having nullified an English attack that was so exhilarating in last week's thrilling victory over France, Ireland struck with one of the best lineout moves you are likely to see.
Number eight Conan popped out of the line and sprinted to the back to tap down a long Rob Herring throw, with a leaping basketball-like pass finding the onrushing Earls who brilliantly sidestepped May to go over in the corner.
Ireland's attack, the focus of much criticism after being largely ineffective so far under Farrell, was back to its patient, probing best and Conan grabbed a deserved second try five minutes from the break.
After 16 phases, Sexton hung up a kick that was brilliantly fielded by fullback Hugo Keenan 10 metres from the line, giving the hosts enough momentum for the Leinster man to pick the ball up from the back of the ruck and spot a gap.
Silly England errors and poor discipline continued early in the second half and they were lucky that the hosts were not out of sight when a second fine Earls try was chalked off for a knock on. Two Sexton penalties were just as good.
Aki's sending off for a high tackle, his second for Ireland in 18 months, and Youngs quick response did little to change things. It took Ireland being reduced to 13 men with a Conor Murray yellow card for England to grab another consolation try.
The result left Ireland with 15 points and England on 10.
