Eugenio Suarez also homered and Joey Votto doubled and scored twice for the Reds, who began their road trip with a win following a 6-3 homestand.
Bruce homered for the third consecutive game as part of a four-run fourth inning. He added his second of the night in the sixth to put the Reds up 6-5 and chase Giants starter Jake Peavy.
It was the third multihomer game this season for the Cincinnati slugger and 20th of his career.
DeSclafani (6-0) pitched in and out of trouble and gave up two home runs but continued his strong run since missing the first two months of the season with a strained left oblique.
