In Milwaukee, Don Sutton (5-4) had a no-hitter for six innings and finished with a three-hitter. Teammate Cecil Cooper drove in three runs with a homer and a triple.
Andre Thornton of Cleveland opened the seventh inning with his eighth homer of the season and his first of two in the game. Sutton struck out eight, including Alan Bannister at the end of the eighth inning for his 3,000th career strikeout. It was Sutton's first victory since May 1. He had lost three straight.
Cleveland loser Lary Sorenson (4-6) allowed nine hits before leaving in the eighth inning.
The Brewers took a 2-0 lead in the first when Paul Molitor led off with a single and, one out later, Cooper hit his 12th homer of the season.
Milwaukee got two runs in the third on a single by Robin Yount, a triple by Cooper and a double by Ben Oglivie.
The Brewers scored twice in the eighth on Rick Manning's sacrifice fly and an RBI single by Jim Gantner.
Thornton hit his ninth homer of the season with two out in the ninth.
Sutton, 39, who has pitched five one-hitters and nine two-hitters in his career, became the eighth pitcher in major league history to strike out 3,000 batters. He got Bannister on a 3-2 pitch to end the eighth inning. Sutton leaped into the air and shook his first as his teammates swarmed to congratulate him and the crowd of 46,037 gave him a standing ovation.