Jenkins homered in the fourth to get the Brewers on the board.
Derrick Turnbow was the beneficiary of Milwaukee's two-run eighth. He moves to 1-and-0 on the year by pitching a perfect eighth inning.
Francisco Cordero pitched a scoreless ninth to earn his 15th save.
Micah Bowie took the loss and falls to 0-and-2.
Milwaukee's sixth straight win raises its major league-leading record to 24-and-10. They finished a ten-game homestand 9-and-1 and have won ten of the last eleven.
The Nationals absorb their eighth straight loss and their major league-worst record dips to 9-and-25.