Bogut and Delfino both scored 19 points, pushing the Bucks to their eighth win in nine games. Milwaukee climbed to three games above the .500 mark.
Washington failed to score 20 points in any quarter and shot just 37.8 percent from the field.
Milwaukee built a 51-36 halftime lead and then outscored the Wizards by 11 in the third period. Andray Blatche and JaVale McGee each had 13 for Washington.
Delfino started the first-period run with a short jump shot and Bogut finished it with a dunk. Milwaukee also scored 10 in a row during the third period.
Milwaukee Coach Scott Skiles moved to within three wins of 350 for his career.