Joe Schmidt's Irish team secured a top seeding for the 2019 World Cup draw as a try by lock Iain Henderson after 23 minutes proved the difference between the sides.
While the Eddie Jones coached England improved after being completely dominated in the first half, they failed to make a serious dent in the Irish defence.
England sealed victory in the tournament last week with a 61-21 thrashing of Scotland, but the Six Nations trophy will be awarded to a downcast English team, the third in 16 years to be denied a grand slam in Dublin on the final day of the tournament.
