England scored after 35 minutes when Young swept home first-time past goalkeeper Wayne Hennessey after Stewart Downing beat Joe Ledley wide on the left and delivered a perfect low cross.
It was one of the rare chances either side created in a largely dour, defensive Group G duel, although Wales substitute Robert Earnshaw should have equalised with the goal at his mercy after 76 minutes but 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. If England avoid defeat in their final qualifier in Montenegro on Oct. 7 they will win the group and qualify automatically for the finals.
Wales remain bottom with three points from six games.