Coleman (1-1) yielded only one run on three hits over 6 1/3 innings to notch his first big-league victory in his second career start. The rookie went 4 1/3 innings and absorbed the loss in his initial start last week against San Diego.
DeWitt homered, got two hits and drove in a pair of runs for the Cubs, who won their first game under interim Manager Mike Quade.
Quade replaced Lou Piniella, who retired after Sunday's game.
Tyler Colvin and Alfonso Soriano each chipped in with a pair of RBI to help the Cubs pound out 15 hits and take the first of three-game series of Nationals Park.
Nats starter Livan Hernandez (8-9) was rocked for seven runs on 10 hits over 4 1/3 innings.