Rookie Jordan Montgomery took a no-hit try into the sixth inning, and Didi Gregorius homered to boost the AL East contenders, his third in two games.
Last-place Cincinnati lost for the 10th time in 12 games. Billy Hamilton's bid for a tying extra-base hit in the eighth was thwarted when pinch-runner Zack Cozart, out of the starting lineup to rest his tender quadriceps, hobbled into third.
Back in the Bronx for the first time since the All-Star break, the Yankees brought along Frazier and relievers David Robertson and Tommy Kahnle, all acquired last week in a trade with the Chicago White Sox.
