Scherzer (5-3) retired nine consecutive batters before Nick Punto led off the seventh with a walk, forcing the right-hander from the game. He allowed three runs and seven hits in his third consecutive victory, closing out a strong May.
Young hit a solo drive in the eighth to make it 5-3, then added a run-scoring single in the ninth.
Jarrod Saltalamacchia hit his 10th homer for Boston, which was seeking its first four-game sweep against the Tigers since 2004. Josh Beckett (4-4) allowed four runs and a season-high 10 hits in seven innings.
The Red Sox opened May with eight losses in nine games to drop to 12-19 on the year. But they closed out the month with a 14-6 run to pull within three of the division lead.
Young and Quintin Berry each had three hits for Detroit, which finished with 14 overall. Berry also scored two runs and stole two bases.
Saltalamacchia connected in the second inning, and Scott Podsednik doubled in Ryan Sweeney to make it 2-0. Detroit responded with three runs in the third, capped by Prince Fielder's two-out RBI single.
Saltalamacchia tied it with a two-out RBI single in bottom half. But the Tigers grabbed the lead for good when Miguel Cabrera singled in Berry in the fifth.
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