Torii Hunter delivered an RBI single in the first inning for the Tigers, playing their first game against the defending champion Red Sox since losing last year's American League Championship Series in six games.
Detroit has baseball's best record at 25-12, having won 13 of its last 16 games and nine in a row on the road.
Scherzer (6-1) is a major reason why.
The reigning AL Cy Young Award winner allowed just three hits over six-plus innings in winning his sixth straight start and lowering his league-leading ERA to 1.83. The right-hander struck out seven, walked four and was removed after yielding a leadoff single to Mike Carp in the seventh.
The game was delayed 47 minutes by rain in the top of the fourth inning.
It barely slowed Scherzer, but definitely put a damper on the marquee matchup of aces.
Scherzer struck out four straight while facing the minimum through three innings before David Ortiz recorded Boston's first hit with a two-out single in the fourth.
David Ross singled to begin the sixth but was stranded on third when Scherzer fanned Napoli to preserve the lead.
Lester (4-5) exited the game after five innings and 94 pitches. He gave up just one run on four hits with seven strikeouts and three walks.
The left-hander labored through a 27-pitch first inning.
Boston's bullpen permitted just two hits, both singles.
NOTES: Lester and Scherzer had faced off just once before, on Sept. 3, 2013, in a 2-1 Boston victory. Lester earned the win, allowing one run in seven innings with nine strikeouts and no walks. Scherzer yielded two runs over seven innings. . Cabrera entered the game batting .522 (12 for23) with one homer in his career against Lester. He went 0 for 2 with a walk Friday. . Ortiz's fifth-inning single extended his season-long hitting streak to nine games. . Detroit reliever Evan Reed was called for a balk in the seventh.