Tries by Bowe and Keith Earls helped Ireland into a 13-6 lead as the final quarter approached before a converted first Test try from England prop Dan Cole tied the match at 13-13.
Man of the match Jamie Heaslip said that the scoreline reflected the balance of the match.
"I think the score is a fair reflection given that we scored three tries to one," said the 26-year-old Israel-born No 8.
"We didn't do much of that when we got back together again last weekend," said Heaslip, who was winning his 24th cap.
It was the third goalkick Wilkinson, Test rugby's world record points scorer, had missed in the match to set alongside his three failures during England's uninspiring 17-12 win over Italy last time out.
But opposing fly-half Jonathan Sexton aided England's cause by missing four out of his five goalkicks and with 10 minutes left he was replaced by the more experienced Ronan O'Gara.
However, before O'Gara could influence the match, Wilkinson kicked England into a 16-13 lead with a drop-goal.
But just when it seemed England were about to win, Bowe from a quick pass by scrum-half Tomas O'Leary, burst through on Wilkinson's inside for his second try which O'Gara converted to leave the visitors four points in front with barely three minutes left.
England pressed hard for a match-winning try but Ireland held out to preserve their hope of a successful title defence.
Ireland led out by prop John Hayes as he became the first player to win 100 caps for the country, didn't have long to wait for the game's first points with a fourth minute try.
Wilkinson, making a rare line break, was tackled in midfield by Earls and prop Cian Healy.
From the turnover, the ball was worked out to Sexton.
Winning only his third cap, Sexton then produced a superb grubber kick behind the England defence and right wing Bowe outpaced flanker Lewis Moody for a well-worked try in the corner.
Sexton missed the difficult conversion but Ireland were 5-0 ahead and, to make matters worse for England lock Simon Shaw had to go off with what appeared to be a left shoulder injury.
Sexton saw a penalty from inside his own half fall just short before, from closer range, he extended Ireland's lead to 8-3.
Wilkinson then kicked his second penalty to leave Ireland with a narrow 8-6 advantage at half-time before both fly-halves missed penalty attempts.
When England scrum-half Danny Care lost his temper with Ireland counterpart Tomas O'Leary at a scrum, Ireland kicked the subsequent penalty deep into English territory.
They won the resulting lineout and quick ball from O'Leary and Sexton saw an overlap created out wide for Earls who crossed for a 56th minute try.
Sexton sliced the conversion attempt but Ireland were now 13-6 in front.
England, seemingly galvanised by the realisation they were heading into the final quarter laid siege to the Ireland line with some typical driving forward play which eventually, after South African referee Mark Lawrence consulted the video official, led to a try for Cole.
Final Score England 16 (6) Ireland 20 (8)
Scorers
England
Tries - Cole
Pen - Wilkinson 2
Con - Wilkinson
Drop - Wilkinson
Ireland
Tries - Bowe 2, Earls
Pen - Sexton
Con - O'Gara
Drop -
Referee: Mark Lawrence (RSA)
Teams (15-1)
England
Delon Armitage; Mark Cueto, Mathew Tait, Riki Flutey, Ugo Monye; Jonny Wilkinson, Danny Care; Nick Easter, Lewis Moody, James Haskell; Steve Borthwick (capt), Simon Shaw; Dan Cole, Dylan Hartley, Tim Payne
Replacements: Lee Mears, David Wilson, Louis Deacon, Joe Worsley, Paul Hodgson, Toby Flood, Ben Foden
Ireland
Geordan Murphy; Tommy Bowe, Brian O'Driscoll (capt), Gordon D'Arcy, Keith Earls; Jonathan Sexton, Tomas O'Leary; Jamie Heaslip, David Wallace, Stephen Ferris; Paul O'Connell, Donncha O'Callaghan; John Hayes, Rory Best, Cian Healy
Replacements: Sean Cronin, Tony Buckley, Leo Cullen, Shane Jennings, Eoin Reddan, Ronan O'Gara, Andrew Trimble
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