Holders Wales, who beat France 27-6 on Friday, the French, England and Ireland all have four points after three matches.
England coach Stuart Lancaster, whose team denied Ireland the Triple Crown, hailed his team's ability to absorb pressure and come back from behind to win a match that makes them marginally favourites to beat Wales at home in a fortnight.
"We showed maturity in seeing the game out, given the experience and quality of the Ireland team," Lancaster said. I think the main quality was not panicking after going behind.
"We made a slow start against New Zealand (in November's defeat) and we made a slow start against France (three weeks ago) and we came back into the game, we kept our composure and I think our ambition to play paid off with the try by Danny Care."
Former England coach Clive Woodward, whose side won the World Cup in 2003, said Lancaster's team were on the right track for the 2015 tournament they will host.
"That is the most significant win for this current England team... that was a defining moment. I think England will really go on now and become something special," he told the BBC.
"I think the England versus Wales game is absolutely huge but I just can't see this England team losing now."
Ireland have the easier task on paper in two weeks' time when they face bottom team Italy, who earlier lost 21-20 to Scotland in Rome, but Ireland coach Joe Schmidt warned taking the Italians lightly would be dangerous.
"We were not so secure today, we must make sure in our next step to be as secure as can be," Schmidt said.
"(Italy) will be devastated today and that makes them more formidable in two weeks' time," he said after Italy had victory over the Scots snatched away by a drop goal in the final minute.
Saturday's game at Twickenham was opened up in the second half by attacking runs from the fullbacks after England led 3-0 at the interval from the first of flyhalf Owen Farrell's two penalties.
Ireland number 15 Rob Kearney touched down under the posts early in the second period after taking a short pass from number eight Jamie Heaslip, flyhalf Jonny Sexton making the easy conversion.
A Sexton penalty put Ireland 10-3 ahead with 30 minutes remaining before Farrell narrowed the gap with another penalty.
England went back in front when fullback Mike Brown broke through in midfield. He took a pass from captain Chris Robshaw and, as he was tackled, fed Care who scampered over the line.
Farrell extended the lead to three points with a conversion in front of the posts and the hosts held on to claim victory.
Overall, the action was far more exciting and absorbing than the scoreline suggests with both sides frequently going close to a try in the first half.
England crossed the line after five minutes and left wing Jonny May, who joined an attack on the right, broke through only to lose the ball as he was about to touch down.
Ireland, having withstood an early onslaught, then enjoyed a period of sustained pressure and gradually pushed the home team back against their line.
There was enterprising running from both sets of backs, especially the Irish who attempted short kicks ahead and crossfield kicks behind the defence looking for the breakthrough.
England ran at Ireland directly while the visitors relied more on criss-cross moves.
The home side had marginally the better of the forward battle with Ireland giving away penalties, the first within kicking distance converted by Farrell from the right to break the deadlock after 25 point-less but entertaining minutes.
The England flyhalf missed another penalty from the left as the interval neared, the ball glancing off the outside of the left upright.
England lost number eight Billy Vunipola with a leg injury in the final minute of the half and he was replaced by Ben Morgan.
