With the bases loaded, Victor Martinez delivered a double off the Green Monster to score Torii Hunter and Miguel Cabrera.
That gave the Tigers the 2-1 lead through six innings.
The Red Sox scored in the 5th inning when Xander Bogaerts' two-out double kept the inning alive. Next batter, Jacoby Ellsbury, brought the 21-year-old rookie home on base hit to right.
Max Scherzer has pitched 6 innings, allowed 3 hits, 1 earned run, and struck out 7.
Scherzer pitched out of a jam in the 6th, when there were runners at second and third with one out, but he got Mike Napoli to strike out and Saltalamacchia to pop up to end the inning.