Replacement flanker Joe Worsley sealed England's victory twominutes from time with their third try as the world and Six Nations championsbounced back from their Twickenham defeat last time out against Ireland.
Fly-half Olly Barkley landed six goalkicks out of seven on hisfull England debut to help restore his side's RBS Six Nations title hopes.
Wales managed two tries through Gareth Thomas and Mark Taylor withtheir other points coming from the boot of Stephen Jones but defeat meanttheir third loss in four Six Nations games this season. "It has been hard week. In the first half we played well butmade a couple of mistakes," said Cohen.
"The key to it was keeping the ball and that was what wedidn't do in the first half. It was good persistence and it paid off.
"I think everyone had something to prove. We all took theblame last week (after the defeat to Ireland) as it was not quite right. This week we trained hard and had a good look atourselves."
After an early break by Wales centre Tom Shanklin, a late call-upin place of the injured Iestyn Harris, England took the lead in the sixthminute.
England full-back Jason Robinson's clearance kick set up a Waleslineout inside their own 22. But they failed to win clean possession and England scrum-halfMatt Dawson launched an attack. The move was carried on by fit-again lock DannyGrewcock in one of several barnstorming first-half runs.
He fed centre Will Greenwood whose pass came to left wing Cohenwho held off full-back Gareth Thomas and flanker Jonathan Thomas to just scorein the corner having been narrowly denied a similar try against Ireland lasttime out.
Fly-half Barkley, making his first England start following PaulGrayson's calf injury, nailed the tricky conversion on a windswept afternoonand England were 7-0 up.
Their lead was soon reduced when Stephen Jones, from just insidehis own half, landed a magnificent penalty - the first of three in theopening 40 minutes.
England, in marked contrast to the Ireland game, were winningtheir lineout ball while recalled flanker Chris Jones was putting in some crunchingtackles.
Jones got Wales to within four points of England with his thirdpenalty before Barkley, whose left-footed kicking style was reminiscent ofinjured World Cup hero Jonny Wilkinson, landed his fourth goal-kick out offour from 47 metres on the stroke of half-time to give England a 16-9 intervallead.
England lost Jones at half-time and soon saw their advantagereduced as well when two minutes into the period Wales exploited a three-manoverlap with prop Duncan Jones sending in Gareth Thomas in at the right corner fora try which tied Ieuan Evans's Welsh record of 33.
But Wales, as they had done in their World Cup quarter-finaldefeat by England, were excelling in broken play with England's pack notretaining possession and setting up drive after drive.
And it was from just such a fragmented situation that Wales tookthe lead. England hooker Steve Thompson's sliced clearance kick set up a Welshcounter with wing Shane Williams bursting through the English cover beforesending in centre Mark Taylor for a try.
Jones was again off target but at 21-16 Wales were ahead for thefirst time in the game.
England eventually regained their composure, as they had donein Brisbane, and started to build some pressure with Cohen denied a tryyards from the line by desperate Welsh defence.
Wing Josh Lewsey went close with a scything run before he washauled down but England's pressure told when Cohen got his second try from barelya foot out following a ruck in the 65th minute. Barkley converted and England were 23-21 up.
Entering the final 10 minutes England were encamped in Wales's 22and the visitors defence cracked in the 72nd minute to give Barkley a simplepenalty 10 metres out which made it 26-21 to the hosts.
Robinson's mesmeric run from deep inside his own half followingthe re-start took England into the Welsh 22 And then Worsley nailed England's victory with a close-range try.Barkley missed his first goalkick of the match but it made no difference.
England: Jason Robinson (Sale); Josh Lewsey (Wasps), Will Greenwood(Harlequins), Mike Tindall (Bath), Ben Cohen (Northampton); Olly Barkley (Bath),Matt Dawson (Northampton); Lawrence Dallaglio capt (Wasps), Richard Hill(Saracens), Chris Jones (Sale); Ben Kay (Leicester), Danny Grewcock (Bath); PhilVickery (Gloucester), Steve Thompson (Northampton), Trevor Woodman(Gloucester). Replacements: Joe Worsley (Wasps) for Jones 41min; Julian White (Leicester) for Vickery 73 min;Mike Catt (Bath) for Greenwood 78 min.
Wales: Gareth Thomas (Celtic Warriors); Rhys Williams (Cardiff), MarkTaylor (Llanelli), Tom Shanklin (Cardiff), Shane Williams (Neath-Swansea);Stephen Jones (Llanelli), Gareth Cooper (Celtic Warriors); Dafydd Jones(Llanelli), Colin Charvis capt (Tarbes), Jonathan Thomas (Neath-Swansea);Michael Owen (Dragons), Brent Cockbain (Celtic Warriors); Gethin Jenkins(Celtic Warriors), Robin McBryde (Llanelli), Duncan Jones (Neath-Swansea). Replacements: Gareth Llewellyn (Neath-Swansea) for Cockbain 28 min: Dwayne Peel (Llanelli) for Cooper 61 min; Ben Evans (Cardiff) for Jenkins 65 min;, Martyn Williams (Cardiff) for J Thomas 68 min; CeriSweeney (Celtic Warriors) for 69 min.
Referee: Andrew Cole (AUS).
AFP - 2004.