Washington closed within 11 to begin the final period, but managed only 14 points in the last quarter to remain winless in three games.
Detroit, Minnesota and the Wizards are the only teams left in the young NBA season without a victory. Boston, Memphis, Dallas, Utah and Phoenix all recorded their first win Friday.
Jennings scored 22 points in pacing the Bucks to their second victory in three games. Andrew Bogut had 13 points and 15 rebounds.
Milwaukee will go on a five-game road trip that begins Monday in Denver.
Washington got 24 points off the bench from Jordan Crawford. Milwaukee shot 53 percent from the field and survived 20 turnovers.