The World champions simply had to win. Two consecutive home defeats would have shattered their status so early in their reign, the prospect was unacceptable to the players, fans, and coach alike.
And in the end, ten points separated Wales and England - breathing space - just enough for the 70,000+ plus crowd to leave Twickenham with bowels intact.
That may not have been the case midway through the second half, two Wales tries had given the visitors the lead, and they looked more than capable of finding space against an extraordinarily narrow English defence.
The storm was weathered, England's forwards eventually gaining the upper hand at the set piece and in the loose, and the final 15 minutes were a 'backs to the wall' defensive effort for Wales.
Northampton wing Cohen took his international tally to 28 touchdowns with a try in each half to win the plaudits and earn the RBS Six Nations Man-of-the-Match.
Rookie fly-half Olly Barkley, making his first Test match start, slotted 16 points from four penalties and two conversions, while substitute flanker Joe Worsley added a last-minute try wide out.
But Wales were always in contention, wiping out a 16-9 interval advantage to lead 21-16 before Cohen and Barkley inspired a late England rally.
The victory means that England will almost certainly retain their Six Nations title on points difference if they beat France in Paris next Saturday.
Wales can only look forward to a tournament finale against Italy in Cardiff next weekend - coach Steve Hansen's last match in charge before he returns to New Zealand.
They made England work for victory though, and the Welsh performance proved in stark contrast to recent appearances at Twickenham, when England posted an average of 50 points a time.
Wales, who came so close to ending England's World Cup ambitions, returned to haunt them at Twickenham, claiming tries from full-back Gareth Thomas and centre Mark Taylor.
Thomas's touchdown put him level with Ieuan Evans' Welsh record of 33 Test tries, and, with a little more luck, Wales might have claimed their first Twickenham triumph since 1988.
The scrum - much maligned after the mualing it took against France - was much improved, and the backline minus Iestyn Harris still had enough invention and gas to cause England problems.
The ten-point cushion would have pleased mo-one more than Sir Cliev Woodward, for he knows, as all fans did, that it could very easily have been the other way round.
Signs that Wales are improving are for all to see, Hansen now faces the banana skin of the Azzuri in the Millennium Stadium next week, in - despite the 1-3 win loss record, a good Six Nations competition for Wales.
Tries: Cohen 2, Worsley
Cons: Barkley 2
Pens: Barkley 4
Tries: Thomas, Taylor
Pens: Jones 3
England: Robinson, Lewsey, Greenwood, Tindall, Cohen, Barkley, Dawson; Woodman, Thompson, Vickery, Grewcock, Kay, Jones, Hill, Dallaglio (capt).
Replacements: Regan, White, Borthwick, Worsley, Gomarsall, Catt, Simpson-Daniel.
Wales: G Thomas, R Williams, Taylor, Shanklin, S Williams, S Jones, Cooper, D Jones, McBryde, Jenkins, Cockbain, Owen, J Thomas, Charvis (capt), D Jones.
Replacements: Davies, Evans, Llewellyn, Williams, Peel, Sweeney, Robinson.
Referee: Andrew Cole (Australia)