Brewers outlast Sox in 11 innings, 7-6
With one out in the 11th, Davis reached on a ground-rule double against Burke Badenhop (0-1) and scored one batter later on Schafer's shot into the left-center field gap.
Francisco Rodriguez struck out all three batters he faced to record the save, preserving the win for Tyler Thornburg (1-0) - one of six Milwaukee relievers who did not allow an earned run.
Carlos Gomez and Mark Reynolds homered for the Brewers while Jean Segura and Aramis Ramirez each notched three hits. Mike Napoli had a three-run homer for the Red Sox, who also received a productive game from Xander Bogaerts (2-for-4, two runs).
After Milwaukee scored a first-inning run, each team plated two runs in the second and three runs in the third.
The final runs of that sequence came on Napoli's three-run shot that drew Boston within 6-5, which remained the score until Segura committed a sixth-inning error that allowed the tying run to cross the plate.
Gomez, Schafer, Reynolds and Scooter Gennett each had two hits for Milwaukee, which played without star outfielder Ryan Braun (thumb).
The Brewers overcame 18 strikeouts, including four by Reynolds, to defeat the Red Sox for the second straight day.
GAME NOTEBOOK: Red Sox 3B Will Middlebrooks was a late scratch due to a leg cramp. ... Red Sox starter Clay Buchholz allowed a career-high 13 hits and six runs over 4 1/3 innings while Milwaukee hurler Wily Peralta gave up five runs (two earned) over five frames. ... The Boston bullpen recorded 15 strikeouts in 6 2/3 innings.