In Anaheim, Calif., Andre Thornton hit a two-run homer and rookie right-hander Don Schulze pitched a nine-hitter for Cleveland against California.
The Angels fell to two games behind first-place Minnesota in the American League West Division.
Thornton's 31st homer of the season ended a three-run rally in the first inning against right-hander Ron Romanick (10-12), who is winless since July 31 and had been passed over for a start the previous time through the Angels' rotation.
Brett Butler led off the game with a single and stole second, his 45th steal, before Julio Franco knocked him home with a single to right. After Mel Hall struck out, Thornton homered over the left field wall on a 1-0 pitch for his 92nd and 93rd RBI of the season.
The Indians made it 4-0 in the fifth when Butler's sacrifice fly to center field scored Chris Bando, who had doubled to right with one out and gone to third on Mike Fischlin's single to left.
Schultzte was struck a glancing blow to the head by a line drive off the bat of Brian Downing in the second inning.
The Angels got four hits in the fifth inning for both of their runs off Schulze (3-5). Rob Wilfong led off the inning with his sixth homer. Bob Boone singled, took second on pinch hitter Rick Burleson's ground out and scored on Derrel Thomas' single.
Schulze walked three and struck out five in the second complete game of his career.