Forward Iain Henderson scored the only try of the game for the Irish midway through a first half they dominated, while Jonny Sexton contributed eight points to help see Joe Schmidt's side over the line.
England's Owen Farrell kicked three penalties to keep Eddie Jones' men within striking distance, but they ultimately came up short in their bid to not only secure a second straight Grand Slam but also surpass New Zealand's record of 18 consecutive Test victories, a sequence they equalled after last weekend's victory over Scotland.
The 2003 world champions had already wrapped up the Six Nations title ahead of the match but victory for Ireland meant they finished second in the standings, five points behind the Red Rose and level on points with third-placed France and Scotland, who ended up fourth.
England captain Dylan Hartley admitted after the match that his side were well beaten on the day, and he believes the result and performance shows his team are still a work in progress despite their recent exploits.
"We are disappointed. We had high hopes, high expectations. But it goes to show we are not quite there as a team," he said. "Credit to Ireland. I think it was negative upon negative, we backed one error up with another."