Dodgers closer Yhency Brazoban (2-4) gave up Tucker's homer on a 2-2 pitch.
Scott Eyre (2-1) pitched a scoreless eighth inning for the victory. He has not allowed an earned run in 20 1-3 career innings against the Dodgers, spanning 27 appearances. LaTroy Hawkins got three outs for his fifth save in nine attempts.
Jon Garland pitched six effective innings and became the American League's first 14-game winner as the Chicago White Sox completed their first four-game sweep in Cleveland in 42 years with a 4-0 win over the Indians on Sunday.
Tadahito Iguchi and A.J. Pierzynski hit home runs for Chicago, which improved to 30-5 against the AL Central and swept a four-game set in Cleveland for the first time since August 1963.
Garland (14-4) allowed seven hits and two walks. He struck out two. Neal Cotts and Cliff Politte completed the eight-hitter.
The Indians hit just .120 (3-for-25) with runners in scoring position in the series. They have lost a season-high five in a row and nine of 10. Cleveland has trailed in 35 of 36 innings since the All-Star break and has not held a lead since the fourth inning in New York on July 10 -- 41 innings overall.
Scott Elarton (6-4) gave up four runs and eight hits over 7 innings.
Royals 5, Tigers 0
At Detroit, Runelvys Hernandez allowed two hits through five innings before he was ejected after triggering a bench-clearing brawl in the sixth inning of a Kansas City win.
Three relievers finished the six-hitter for the Royals, who had three players and manager Buddy Bell ejected in the melee that started after Hernandez beaned Detroit's Carlos Guillen in the helmet, his third hit batter of the game. Guillen and two other Tigers were tossed.
Angels 2, Twins 1
At Minneapolis, John Lackey tied a career high with 10 strikeouts and Jeff DaVanon homered to lead Los Angeles over Minnesota.
Lackey (7-4) scattered five hits over seven innings and allowed just the one unearned run in a dominant performance to win for the first time in four starts.
Francisco Rodriguez pitched the ninth for his 20th save in 22 chances.
The Seattle Mariners activated infielder Dave Hansen from the 15-day disabled list after Sunday's game against Baltimore, sending outfielder Chris Snelling back to Triple-A Tacoma.
Hansen, hitting .194 in 25 games, went on the disabled list on July 3. Considered one of the game's best pinch hitters, he joined the Mariners for the second time in two seasons on May 3.
Snelling was called up on July 3 when the Mariners designated Bret Boone for assignment. He appeared in four games, going hitless in five at-bats. He walked on July 6 in his first major league plate appearance since June 2002, missing the 2004 season after several injuries.
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