Young struck after 35 minutes when Stewart Downing beat Joe Ledley wide on the left of the Welsh defence and sent a perfect low cross for Young to sweep home first time past goalkeeper Wayne Hennessey.
It was one of the rare scoring opportunities either side created in a largely dour, defensive Group G duel although substitute Robert Earnshaw, who had only been on the field for nine minutes, should have equalised for Wales with the goal at his mercy after 76 minutes. Instead he fired high over the bar.
The result took England to 17 points from seven matches, six clear of Montenegro who have 11 from six.
England's final qualifier is in Montenegro on October 7 and if England avoid defeat they will win the group and qualify automatically for the finals. Wales remain bottom with three points from six games.
After a slow start by both teams Wales settled into a defensive shape and frustrated England for the first 35 minutes until Young scored.
They also finished the more adventurous team and could even have stolen a share of the spoils with better finishing and luck.
Before the goal there was little action in either penalty area and the match was in complete contrast to England's pacy 3-0 win over Bulgaria on Friday or Wales revitalising 2-1 win over Montenegro on the same night in Cardiff.
Instead Wales appeared to be intent on damage limitation and restricted England to a skied bicyle-kick by Downing after 28 minutes, although Wayne Rooney tried an ambitious chip from 30 metres which also went over the bar.
Wales, well beaten by England 2-0 in Cardiff in March but vastly improved since then, were more resilient playing with nine or 10 men back and only Steve Morison a distant figure alone up front.
But without the suspended Craig Bellamy, they were toothless in attack, hardly challenging opposing goalkeeper Joe Hart who was a virtual spectator, without a serious shot to save in the opening period.
Wales never looked like beating England for the first time since 1984 or winning at Wembley for the first time since 1977, but they did make England work hard for the three points.
The second half was better for the home side with James Milner making some telling runs from deep, but with Rooney largely shackled and Young isolated on the wing, England had no time to relax.
Midfielder Frank Lampard, left out of the starting line-up on Friday, returned to win his 88th cap and did well in carrying the game forward to the Welsh, whose heavy reliance on Gareth Bale to create their own chances was thwarted by some sterling midfield work by Gareth Barry and Gary Cahill.
Wales have not scored a goal against England in the four matches they have played against them since their last victory at Wrexham in 1984, but Earnshaw should have done so but for an astonishing miss from five metres out 14 minutes from time.
If that had gone in, it would have given Wales a merited draw but on balance, England just did enough to win at Wembley for the first time in five matches over the last 12 months and move to within touching distance of the fina
