The Royals tied a club record with 24 consecutive scoreless innings, which was set June 9-12, 1976. That streak ended in the seventh when Brandon Phillips' two-out double off reliever Ryan Madson scored Zack Cozart.
The Royals, who won for the fifth time in six games, improved to 26-14, the franchise's best record after 40 games.
The Reds lost their fifth straight, a season high.
Guthrie (4-2) pitched out of a bases-loaded, one-out predicament in the first inning and won his third straight start. He gave up five hits, walked two and struck out three. Guthrie retired 13 on fly balls and two on grounders.
 
Guthrie throws 6 scoreless innings; Royals top Reds 7-1
 
Reds right-hander Jason Marquis (3-4) was pulled after 3 2-3 innings, yielding four runs, four hits, two sacrifice flies, two walks and a wild pitch. In losing his past three starts, Marquis has surrendered 21 hits and 15 runs in 12 1-3 innings for a 15.33 ERA.
Mike Moustakas, who hit .212 last season, had three hits for his 16th multi-hit game to raise his average to .342.
Kendrys Morales and Alex Gordon drove in two runs each. Morales' 32 RBIs ranks second in the American League.
Phillips had three of the Reds' nine hits.
 

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