Cingrani (2-0), making his third major-league start, allowed only two hits and a walk, enabling the Reds to avoid a four-game road sweep at the hands of the Nationals.
Aroldis Chapman was called on to make his fifth save after the Cincinnati bullpen had allowed a pair of runs.
Brandon Phillips delivered a two-run hit in the first inning, putting the Reds ahead to stay, and Zack Cozart went 2-for-3 with a pair of RBI en route to the victory.
Joey Votto provided a run-scoring among his two hits for Cincinnati.
Washington starter Ross Detwiler (1-2) was tagged for four runs (three earned) on 11 hits over five full innings.
Ian Desmond went 2-for-4 with an RBI in the loss.