The homer, Young's 15th this season and his only hit in the game, gave Arizona a 5-0 lead with no outs in the top of the fourth.
The winner was starter Doug Davis (9-14).
Juan Gutierrez hurled a 1-2-3 ninth, earning his ninth save.
Sam Fuld had two of six hits, including a two-run first-inning homer, for the Cubs, who lost twice in the three-game series and finished second in the National League Central.
The losing pitcher was starter Ryan Dempster (11-9).