Wilson (11-5) allowed only one run on four hits and one walk in 7 2/3 innings, and fanned eight en route to his third win over Boston this season.
Young's clout in the seventh inning put the first-place Rangers ahead 5-0 and guided them to a victory in the rubber match of a three-game set with the Red Sox.
Julio Borbon went 2-for-3 with a pair of RBI and Andres Blanco drove in a pair for Texas.
Daisuke Matsuzaka (8-4) took the loss for Boston, yielding four runs on seven hits over 6 2/3 innings.
Darnell McDonald connected on a two-run homer for the Red Sox.
2014: The Year in Music [PHOTOS]