"I pitched one of my best games because I was able to throw more strikes with all my pitches," Rosado said. "Today I was using all my pitches and I wasn't afraid to throw back-to-back changeups."
Rosado (7-9) struck out six and walked one. He walked Randy Winn and hit Quinton McCracken leading off the first, then retired the side in order during five of the next six innings.
"The first inning been a crucial inning a lot this year," Royals manager Tony Muser said. "Rosie got through it, built some momentum and did a great job of pitching. That's as good as I've seen him pitch, keeping the ball down with all of his pitches."
Jeff Montgomery finished for his 28th save in 32 chances, allowing Fred McGriff's 15th homer.
Kansas City is one shy of its season-high four-game winning streak (May 24-29). The Royals have won seven of 10 games against Tampa Bay, including all four in Florida.
"We always end up playing Tampa Bay after we've played Boston and New York. They're a little more in line with our level of ability and talent," Montgomery said. "When we play against the giants, regardless of who you play, after those it seems like much less of a task to win a ballgame."
The Devil Rays (49-78), who have lost five of six and dropped a season-high 29 games under .500.
Terry Pendleton and Jermaine Dye put Kansas City ahead 2-1 with two-out, RBI singles in the fourth, and Dean Palmer homered off Esteban Yan in the ninth. Palmer homered for the second straight game, raising his total to 29, including four against Tampa Bay.
Wilson Alvarez (5-13) allowed two runs and five hits in seven innings, striking out eight and walking two.
"If you hold a team to two runs in seven innings, you've done a pretty good job," Devil Rays manager Larry Rothschild said. "You should have an opportunity to win the game."
Alvarez had struggled in his previous four starts, allowing 19 runs in 23 2-3 innings. Since coming off the disabled list July 6, he has won once in nine decisions.
"I haven't pitched like this in a long time," said Alvarez, sidelined almost two months by left shoulder tendinitis. "I did my job. I gave the team a chance to win."
Third inning doubles by Kevin Stocker and McCracken put the Devil Rays ahead 1-0. Rosado retired 13 straight following McCracken's hit.
McCracken had two assists, giving the left fielder 16 this season. Tampa Bay outfielders have 39.
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