England were on top for most of the game but led by only five points until Ollie Lawrence scored their third try five minutes from time.
Their first win in Cardiff since 2017 should have been by a greater margin as Wales barely threatened and scored a solitary try through a Louis Rees-Zammit intercept at the start of the second half.
After the free-flowing action in Ireland's victory over Italy in the early kick off the game in Cardiff felt considerably more conservative but for the victorious coach involved the result was everything.
"I thought first half our intent to try and get the ball to the edge, that was an improvement," said England coach Steve Borthwick.
"It didn't keep going like that. It turned into a pressure contest. Clearly our breakdown needed to be better and you’ve got to credit the Welsh jacklers. But as we’re in this process, we need to keep these players growing.
"There were bits in that performance that we can really push on with. We’ve got two big games to finish the Championship (at home to defending champions France and away to leaders Ireland)."
Borthwick recognised the physical and mental effort of the Welsh team, who had lost their first two games heavily and spent much of the last week negotiating with their union while threatening a strike that would have forced the postponement of Saturday's game.
"Those Welsh players deserve such enormous credit and respect to go through what they've gone through and put in a performance like that," Borthwick said.
England captain Owen Farrell added: "It was a different challenge for us to come away from home to a place like this, a team that has had a lot going on during the week and have unified to come together for this crowd at the weekend. Fair play to them.
"We had a job to do and thankfully we took a step forward. We had a job to do, and we've done it. It was a good Test for us. We stuck in there and fought until the end and I thought we took control of that last 20 minutes.
"We're only starting, we have another big team coming next time back at Twickenham (France) and we have a lot of work to do. There's bits starting to show, we've laid some foundations and we want to keep building on it all."
