Rob Kearney's try straight after half-time edged Ireland into a 10-3 lead, but England blasted straight back through Care's score and clung on for their second victory of the RBS 6 Nations campaign.
England's win set up a four-way fight for the title, with Stuart Lancaster's men, Ireland, Wales and France all suffering one defeat in the tournament's first three rounds.
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Lancaster's grind eclipsed Joe Schmidt's tactical masterclass as England just about rebuffed Ireland's meticulously-crafted attacking ploys.
England wasted the first try-scoring chance, Jonny May unable to convert after concerted pressure, leaving the clash scoreless at the end of the first quarter.
Mike Brown's marauding midfield line-break yielded a 17-phase onslaught on Ireland's line from the hosts.
Owen Farrell nearly botched a right-wing overlap, before Billy Twelvetrees sent Gloucester club-mate Jonny May into the right corner.
Ireland scrum-half Conor Murray just managed to tip a desperate left hand to the ball as May set to dot down though, denying England the opening score.
Master tactician Joe Schmidt was always going to unleash a few new Irish tricks aimed to outsmart England's powerful pack.
And the first came in the shape of a feigned maul that brought a pinpoint crossfield chip from Johnny Sexton.
Andrew Trimble collected in space, but England immediately recovered to close him down, and deny Ireland a score.
England had already shut out Ireland after neat half-breaks from Cian Healy and Gordon D'Arcy, and gained confidence from their effective scrambling defence.
Farrell's careless late shoulder-barge on Murray gifted Ireland a penalty line-out on England's 22.
Ireland were once more unable to convert their opportunity though, failing to draw dividend by again trying to turn England through tactical kicking.
And when Ireland captain O'Connell illegally shut down the line-out space, the game finally had a score.
Farrell slotted the penalty with ease to hand England the 3-0 lead.
Schmidt's wide-game influence came into play when Ireland tried to stretch England with three run-arounds in one phase, but England were wise to the ruse.
Ireland's clear tactic was to expose Luther Burrell at outside centre, but the visitors could not draw the space for Dave Kearney to cut loose scything back into the 13 channel.
Any scrum dominance for Ireland came to nought when the visiting pack were penalised for a deliberate set-piece wheel.
The unsubtle ploy allowed Farrell a second shot at goal, but the Saracens fly-half struck a post, unable to double England's tally.
Wrecking ball England number eight Billy Vunipola fell awkwardly on his right ankle, and was replaced by Gloucester's Ben Morgan.
England went for the jugular with an attacking line-out on the stroke of half-time, but Burrell's knock-on wasted the platform.
Ireland finally caught England out with one of those Joe Schmidt-inspired plays straight after half-time.
Jamie Heaslip played static fly-half, while his team-mates cut dummy runs all around.
The number eight stood his ground and delayed just long enough for full-back Kearney's perfectly-timed arrival - and the Leinster 15 soared under the posts, bisecting the statuesque Joe Launchbury and Davey Wilson.
Sexton converted to hand Ireland a four-point advantage.
Suddenly the tactics that failed to bear fruit in the first half were all coming good for Ireland.
Sexton chipped in behind May after a quick-tap penalty, the Gloucester wing failed to clear and from the driven line-out Ireland claimed a penalty.
Sexton landed the goal to send Ireland 10-3 ahead.
England rallied, May bisecting the midfield, Farrell cutting a neat break and Danny Care's trademark tap-penalty forcing a drive to the whitewash from Luther Burrell.
Rory Best conceded a penalty under the posts and Farrell slotted his second goal of the game, to cut their deficit to just four points.
Sexton over-hit the restart straight into touch, gifting England an attacking scrum platform they did not waste.
Brown raced through the centre from Robshaw's offload, setting Care free to hare under the sticks for the hosts' first try.
Farrell's conversion put England into a 13-10 lead.
Care's try swept the tie straight back in England's favour, but the hosts failed to force a breakthrough from their next attack.
Jack Nowell shanked a clearance straight into touch and that allowed Ireland to build the phases for just the second time in the half.
O'Driscoll and Sexton mistimed a simple run-around, though, wasting all that build-up with a simple knock-on.
But Ireland forced a turnover at the scrum to win a set-piece of their own on England's 22.
Ireland used the scrum to work a chance to set their maul, gaining an early drive.
Crucially England managed to shut down the shove, though, and win a vital turnover.
And when Conor Murray threw away possession from a loose blind pass off another maul, Ireland's challenge was all but at an end.