PHOENIX (AP) -- The Kansas Royals had given Danny Duffy almost no run support over his previous four starts and little all season, so they were anxious give him something, anything against the Arizona Diamondbacks.
Ten runs on three swings did the trick nicely.
''Our pitching has picked us up all year and for us to give Duffy some support like that, especially a guy we haven't been giving any to, was big for us,'' said Butler, who had three hits his previous game.
The Royals started early, battering Wade Miley (7-8) for 10 runs by the fifth inning.
Salvador Perez had the first big blow with a three-run homer in the third inning and Butler added another three-run shot during Kansas City's eight-run fifth. Aoki capped the big inning with his first career slam, marking the first time the Royals had a grand slam and three-run homer in the same inning.
Kansas City had 10 of its 15 hits - three by Perez - by the fifth inning and had a season-high in runs, allowing Duffy (6-10) to cruise to his first win since June 30.
Not bad for a team that's missing its best hitter (Eric Hosmer) and entered the game with 62 homers in 110 games, by far the fewest in the majors.
''You score 10 runs off of three swings of the bat, you'll take it,'' Royals manager Ned Yost said. ''I'm not really (used to it), but I'll take it when I can get it.''
The Royals have mostly struggled when Duffy has pitched this season, producing 2.34 runs of support, lowest in the majors among pitchers with at least 100 innings. The left-hander had allowed a run or less in 11 of 16 starts, yet was 4-5 in those, including four straight losses.
That changed in a big way against the Diamondbacks and Miley.
Arizona's left-hander had been sharp over his previous six starts, going 4-1 with a 2.45 ERA, including 6 2-3 scoreless innings his last outing.
The Royals hit Miley hard early, starting with Perez's 13th homer in the third inning. Butler added his own three-run shot in the fifth and, after a pair of wild pitches by Miley, Aoki put the capper on the big inning with his first career grand slam on the first pitch by reliever Bo Schultz.
Miley allowed nine hits and walked three.
''Everything I threw was in the middle of the plate,'' Miley said. ''You can't find success up here when you are living in the middle of the plate.''
Duffy got off to a rough start, giving up a pair of doubles in the first inning, including one by Mark Trumbo that scored the game's first one.
The left-hander was sharp after that, allowing three hits and striking out seven in five innings to end a five-start winless streak.
''This was not a good night for us all around,'' Arizona manager Kirk Gibson said. ''We had some opportunities and couldn't come through.''
Royals LF Alex Gordon reached a big milestone in the fifth inning, lining a single for his 1,000th career hit - all with Kansas City. He became the 10th player in franchise history to reach 1,000 hits and joined Butler, seventh on the list with 1,231. ... Trumbo played his 500th career game.
Aoki hit 10 homers as a rookie in 2012 and eight last season, but had yet to clear the fences this season. He finally cleared the wall in the fifth inning, ending a streak that stretched 338 at-bats to Sept. 27, 2013.
''I knew it was coming, somewhere down the road,'' Yost said. ''Glad to see it today.''
Diamondbacks: OF A.J. Pollock, out since June 1 with a broken right hand, was 0 for 5 in his first game with Triple-A Reno. He was 1 for 3 in two games with Arizona's rookie league team.
Royals: RHP Yordano Ventura will start Wednesday's game against Arizona after picking up his eighth win of the season the last time out. He allowed an earned run in seven innings against Minnesota and struck out seven for the second straight start.
Diamondbacks: RHP Josh Collmenter, Wednesday's starter against Kansas City, has allowed nine runs in eight innings over his past two starts.