Arroyo (3-0) allowed a home run on his first pitch, then limited the Brewers to five hits over the rest of his outing. He retired 10 in a row at one point to pin the loss on Sheets (0-2), who struck out 10 in seven innings.
David Weathers pitched a perfect ninth for his fourth save in five opportunities.
Brandon Phillips and Felipe Lopez both used their speed to manufacture runs for the Reds, who had been 1-3 when scoring less than six runs.
Lopez led off the fourth inning by striking out on Sheets' wild pitch. He reached first without a throw and stole his sixth base on the next pitch. Lopez went to third on Adam Dunn's groundout and scored on Rich Aurilia's RBI single.
Phillips led off the fifth inning with a double. Sheets struck out the next two hitters, but couldn't get out of trouble.
Ryan Freel hit a slow bouncer to Corey Koskie, whose throw from third was off target. A stretching Prince Fielder went to the ground to corral the errant throw but Freel reached on the infield single.
Phillips raced around third and beat Fielder's throw home to give Cincinnati a 2-1 lead. Lopez then singled but Sheets struck out Dunn to end the inning.
The Reds tacked on an insurance run in the eighth. Lopez, who finished 2-for-4 and scored two runs, doubled and scored on Scott Hatteberg's RBI single.
Gabe Gross hit Arroyo's first pitch over the right-field wall for his first career leadoff homer. He led off the sixth with a single and reached third but Fielder, with 23 hits in his last 13 games, struck out trying to stop his swing on a high pitch.
The Brewers also had runners in scoring position in the seventh and eighth innings but failed to score.
Sheets, who recorded 10 or more strikeouts for the 11th time in his career, consistently hit 95 mph on his fastball throughout his performance, but failed to record his first win since tearing a muscle in his back Aug. 26. He gave up two runs and six hits.
Sheets struck out 10 or more for the first time since July 4 in a 3-2 victory against Florida. ... Freel extended his hitting streak to eight. ... Brewers manager Ned Yost said that when a pitcher can help himself out at the plate like Arroyo has done so far this season, it can be worth an extra win or two over the course of the season. Arroyo went 0-for-3 with two strikeouts. ... Reds manager Jerry Narron said Phillips has been an "outstanding surprise." Phillips hit two home runs, including his first grand slam, on Thursday night. He was acquired from Cleveland on April 7 for cash or a player to be named. "No one expected him to come in here and have 13 (RBI)," Narron said.