Ireland had ended the previous world record run of the New Zealand All Blacks in Chicago last November
and repeated the feat against England, which was seeking to make history under coach Eddie Jones with a 19th consecutive win.
But his team came up against an inspired home side, which hustled and harried England from start to finish at the Aviva Stadium and scored the only try of the match.
England had clinched the Six Nations title with a crushing 61-21 victory over Scotland last weekend, but defeat with so much at stake was a demoralizing end to its campaign.
"It just wasn't our day today, we just couldn't get our game going," Jones told BBC Sport after the defeat. "I take full responsibility for the loss."
Ireland led 10-3 at halftime against a lackluster visitor, which appeared nervous and below-par in a fiercely partisan atmosphere.
An early exchange of penalties from Jonathan Sexton and Owen Farrell was followed by an Irish try as lock Iain Henderson stretched out to touch over after a forward drive near the line.
Sexton kicked the conversion and an upset looked firmly on the cards at halftime.
England hit back after the interval when Farrell converted a long-range penalty to take his tally of international points to 600, making the 25-year-old just the 26th player to reach the landmark.
Sexton kicked another penalty of his own before Farrell slotted over his third penalty to narrow the gap to just four points.
But in driving rain, England's attempts of a further score were thwarted and Ireland held out to complete a memorable victory after earlier disappointments in the Six Nations this season.
Ireland claimed second place on points difference above France and Scotland, with all three teams having three wins and two defeats.
"The bit of pride we can take is that the three teams that sit above us in the world rankings we have beaten in the last six months," Ireland coach Joe Schmidt said, referring to No. 1 New Zealand, England and Australia.
England lifted the trophy after four previous wins, but it was a bittersweet celebration, with hopes of a 26th Triple Crown ended and its winning run in the Northern Hemisphere tournament halted at 11.
French joy in overtime
In the other matches on the final day of the Six Nations, there was a dramatic 20-18 win for France over Wales in Paris as Camille Lopez converted Camille Chat's try after no less than 20 minutes of stoppage time.
Wales looked set to finish its campaign with a second straight win after its victory over Ireland last weekend, leading 18-13 going into the added time after six penalties from Leigh Halfpenny.
But France kept up the pressure and Chat eventually went over from close range before Lopez made the winning kick.
Earlier, Scotland thrashed bottom side Italy 29-0 at Murrayfield in coach Vern Cotter's final game in charge.