This was a warm-up that did not lack heat. Both camps maintained in the build-up that results were of secondary importance as they counted down to the start of the World Cup in Japan, but the rapture Wales’s players showed in the final minute when they repelled a maul suggested otherwise.

The response of the crowd at the final whistle was even more jubilant. The victory will put Wales at the top when the revised world rankings are published on Monday and if their performance was not that of putative World Cup winners, it again showed how difficult they are to overcome when they are geared up for a scrap.

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They felt they were too relaxed at the start at Twickenham last Sunday, losing the match in a somnolent opening 20 minutes, but here they were fully attentive. It was an afternoon when the result did hold significance for them and not just because their opponents were again only at half strength. The sides could meet in the quarter-finals of the World Cup, depending where they finish in their group, and England are the only Six Nations team that Wales have lost to more than beaten since their head coach Warren Gatland took over 12 years ago.

The one try came when England were down to 13 men in the first half. Anthony Watson, a late replacement for Ruaridh McConnochie, was trudging his way to the sin-bin after receiving a yellow card for deliberately knocking-on to prevent Wales from exploiting a three-man overlap as they counterattacked in their own half. Willi Heinz had just left the field for a head injury assessment and Ben Youngs was waiting to replace him.

As England pondered their realignment, Dan Biggar, who had set up to kick the ball into touch on the left, turned to the other wing and punted long for Josh Adams, who caught the ball and made it into the opposition 22. England eventually scrambled back, but when two phases later Biggar received the ball again, George North was among three players unmarked on the left.

Biggar chipped the ball with the outside of his right foot and North only had to catch it to score his 38th try for Wales, a tally exceeded only by Gareth Thomas and Shane Williams.

It proved to be the difference between the sides and highlighted the tactical importance of Biggar, who recovered his starting place following the long-term injury suffered by Gareth Anscombe at Twickenham.

Wales fielded Josh Adams, rather than North, on the right wing to mark Joe Cokanasiga, and Biggar sent a flurry of kicks along that flank after an early bombardment of Elliot Daly yielded no profit. Wales scrummaged with greater purpose than at Twickenham, and were more accurate in the lineout, where Aaron Wainwright was employed regularly until a dead leg forced him off at half-time.

England conceded penalties under pressure, not least at the breakdown, and while Wales did not aim for the posts until the 26th minute when Biggar gave them the lead, they took on England at their strongest point, at close quarters rather than among the three-quarters. They put a few moves together, but they were preparing for the World Cup when defence is expected to decide matches between the leading sides.

Facebook Twitter Pinterest Billy Vunipola of England is tackled by Tomas Francis and Josh Adams of Wales. Photograph: David Rogers/The RFU Collection via Getty Images

England responded to their 10-point interval deficit by reinforcing their ranks with four Lions early in the second half, including Owen Farrell. Two George Ford penalties brought them close, but they struggled to sustain pressure and their best move was from a lineout just inside their own half when Youngs and George combined to free Watson.

Wales held on, just, relieved when Lewis Ludlam also did so with the ball on the floor to concede a penalty. There were five minutes to go when Leigh Halfpenny kicked a penalty from 45 metres to put his side a converted try ahead shortly after narrowly missing from halfway. Both the full-backs’ efforts had an element of weariness, with a lack of altitude each time, but Halfpenny was only drafted into the side minutes before the start after Liam Williams felt a hamstring tighten and, not being selected on the bench, he had had a gruelling morning training session.

England had one final chance when they kicked a penalty to touch but could not get their driving maul into gear against opponents with by then an unfamiliar back five forward formation. The result apart, Eddie Jones could take at least as much out of the game as Gatland, given the players who were missing. For once there is an air of mystery about England, a sense that a tale of the unexpected may be unfurling.

Jones raised an eyebrow when told Wales had gone to the top of the rankings. Gatland turned a lighter shade of red, saying it was just a number and that “Kiwi journalists will say it is a joke”. He knows only too well that the time to get ahead of New Zealand is a few seconds from the end of the World Cup final.