Manchester United star Young rifled in a low cross from Stewart Downing on 35 minutes to secure all three points for England, who now need only a point from their final match against Montenegro next month to clinch the group.
Wales squandered a golden opportunity to secure what would have been a scarcely-deserved point when substitute Robert Earnshaw missed an open goal from five yards out 15 minutes from time. Earnshaw's miss left Wales manager Gary Speed burying his head in his hands, but the visiting coach could have few complaints with his team's defeat after they failed to seriously test England for long periods.
Young admitted England's players had been disappointed by yet another lacklustre display in front of 77,128 fans at Wembley. "The performance wasn't great but you go out to win the game and that's what we've done," Young said. "We wanted to get the three points to boost our chances of getting top of the group and we've done that."
England manager Fabio Capello agreed his team had been lucky to hang on for a win in light of Earnshaw's miss. "I think we were a bit lucky, they made a big mistake in front of the goal, but that was our luck," Capello said. "Sometimes the result is more important than the other things."
Wales manager Speed was left rueing Earnshaw's missed chance. "I think if you wanted one person in that position it would have been 'Ernie.' But he's a great lad and he's mentally strong and he'll get over that. It's just one of those things," Speed said.
"No-one will be more disappointed than him. I thought it was in. But it's just one of those things. I'm more proud with the way the team played in the second half."
England manager Fabio Capello had recalled Chelsea midfielder Frank Lampard to his starting line-up after dropping him for last Friday's 3-0 victory over Bulgaria in Sofia. Capello also rested Theo Walcott as a precaution, replacing the Arsenal winger with Manchester City's James Milner.
England enjoyed by far the better of the first half, and might have taken the lead after only eight minutes only for captain John Terry to flash a close-range header wide of the post after an inviting corner from Young.
With Wales star Gareth Bale deployed to the right wing, all too often the visitors were left exposed down the opposite flank, where Liverpool's Downing was a constant menace. Downing had fired a warning shot on 17 minutes when he ghosted past fullback Neil Taylor only to overhit his cross. Moments later Downing was on the prowl again, gliding into space but just failing to pick out Wayne Rooney with his centre.
At the other end England goalkeeper Joe Hart was a virtual spectator for most of the first half, although Bale reminded the home side of his latent threat when he beat Milner to draw a booking from the England midfielder. Wales' best moment of the opening half came when defender Chris Gunter went on a rare gallop upfield on 33 minutes only to smash a wild shot 20 yards wide.
Two minutes later England were in front, and again Downing was at the heart of the action, embarrassing Joe Ledley and racing to the byline before crossing for Young who lashed home from close range. England might have had another five minutes later when Young curled in a cross which Rooney just failed to get his head to.
England always looked the more likely to score after the restart, their best chance coming when Lampard scooped his shot over the bar after a powerful surge into the box by Gareth Barry. But they almost paid the price for failing to add to their tally 15 minutes from time only for Earnshaw to suffer a nightmare miss.
A free-kick from Wales captain Aaron Ramsey picked out Darcy Blake on the edge of the six-yard box who got past Barry and squared to an unmarked Earnshaw. With the goal gaping however, the Cardiff striker shot over.