Jim Presley singled with no outs in the ninth inning to score Barry Bonnell as Seattle won at home.
Bonnell opened the ninth with a double off reliever Joe Beckwith (1-3) and scored as Presley hit a 2-1 pitch.
Karl Best (2-1) worked the final 1 1/3 innings to earn the victory.
Kansas City tied the score, 1-1, in the fifth. John Wathan doubled, moved to third on Buddy Biancalana's sacrifice bunt and scored on Willie Wilson's single to right.
The Mariners took a 1-0 lead in the first. Jack Perconte doubled, took third on Phil Bradley's single and scored on Ivan Calderon's double.
Seattle rookie right-hander Billy Swift worked the first 7 2/3 innings.
Kansas City's Bud Black, who pitched the first eight innings, struck out a career-high 10 batters. He became the first Royals pitcher to strike out that many since Rich Gale on June 26, 1983.
Twins 4, Rangers 1: Gary Gaetti and Greg Gagne homered and Ken Schrom pitched a seven-hitter as Minnesota won in Texas.
Gaetti's ninth homer, after Tom Brunansky walked, broke a 1-1 tie in the sixth inning.
Schrom (5-5) did not allow an extra-base hit and walked four in getting his third complete game this season.
Charlie Hough (5-7) lasted six innings. Hough had pitched six straight complete games against the Twins.