Scherzer (8-2) was back in his 2013 Cy Young form, striking out eight and walking three while outdueling Sale (5-1). Only three times did the White Sox have men in scoring position.
Sale was nearly as sharp as Scherzer. He struck out 10 - all swinging - to match a season high and allowed five hits in seven innings.
''He was dominant,'' Sale said of Scherzer. ''You know coming into this, you know who you're going up against and it's not going to be easy.
''For a long time there, it was who's going to flinch first and unfortunately it was me.''
The only run Sale allowed was on Martinez's solo shot into the left field bullpen to lead off the fifth.
''He pitched a great game,'' White Sox manager Robin Ventura said. ''He made one mistake, but that can happen in a game like that.''
Sale didn't allow a baserunner until Rajai Davis led off the fourth with a single and left the game with Detroit leading 1-0.
Scherzer had allowed 20 runs over 26 1-3 innings in his previous four starts, going 1-1. The right-hander pitched nine innings once before in a game, on Sept. 1, 2010, in 2-1 10-inning loss to Minnesota
This time, the nine innings were all the Tigers and Scherzer needed.
''It's awesome,'' said Scherzer, who threw 113 pitches. ''I finally got the monkey off my back.
''I was finally able to go nine and finish the deal, so it's good feeling.''
Martinez, who entered the game second in the AL with .330 average, extended his hitting streak to seven games as the Tigers ended a three-game losing streak and won for just the third time in their last 11. By salvaging the final game of its rain-shortened series against the White Sox, first-place Detroit widened its AL Central lead to 2 1/2 games over idle Kansas City.
Martinez is batting .327 against Chicago in 154 games with 24 homers and is 13 for 25 (.520) against Sale.
Sale rebounded nicely from his previous start, a no-decision last Saturday in Anaheim when he took a three-hit shutout and 5-0 lead into the eighth against the Angels, but then fell apart.
Mike Trout hit a grand slam of Sale in the eight to tie that game at 5 and the Angels went on to win.
''The last game it was about giving up a homer and this game it was about giving up a homer,'' Sale said ''I've just got to be better in that situation.''
Davis led off the fourth with the game's first hit, a smashed, one-bounce single off the glove of White Sox third baseman Conor Gillaspie. But Sale picked Davis off during the next at-bat.
NOTES: Sale struck out at least 10 and walked none for the third time in his career. .. Cabrera moved back to first base after a left hamstring pull restricted him to DH for two games. CF Austin Jackson entered the game with 10 hits in his last 20 at-bats - but is just 2-for-30 lifetime against Sale and didn't start. ''It's just really a good time to give him (Jackson) a day off,'' Tigers manager Brad Ausmus said. ''You want to give guys a day off, generally speaking, against pitchers they don't do as well against.'' Rajai Davis moved to center field and J.D. Martinez starting in left. . Slumping Chicago C Tyler Flowers returned after sitting out Thursday. He entered the game 3 for his last 37. . The White Sox open a series at home against Kansas City on Friday with Jose Quintana (3-6) expected to face Jeremy Guthrie (2-6). The Tigers host Minnesota on Friday with Drew Smyly (3-4) slated to start against the Twins Kyle Gibson (5-5).