Rickie Weeks had three hits and Aramis Ramirez added two doubles for Milwaukee, which twice benefitted from Washington outfielders losing fly balls in the sun.
Washington (92-60) leads the NL East by 4 1/2 games over Atlanta, a 2-1 winner over Philadelphia on Sunday. The Nationals’ magic number to clinch the division remains at six.
Reliever Brandon Kintzler (3-0) pitched a scoreless sixth inning for the win. John Axford recorded the final out with two runners on for his 33rd save.
Losing pitcher Ryan Mattheus (5-3) allowed three earned runs on four hits.
Milwaukee broke a 2-2 tie with a three-run seventh. Weeks singled and Ryan Braun grounded into a fielder’s choice, with Weeks out on a close play at second. Ramirez doubled to right, putting runners on second and third.
After Corey Hart was walked intentionally, Lucroy hit a grounder up the middle. Washington shortstop Ian Desmond made a diving stop, but couldn’t make the play at second and the Brewers led 3-2 with the bases still loaded.
Carlos Gomez hit a fly ball to right that was playable, but Jayson Werth lost it in the sun and Ramirez scored as Gomez was credited with a single. Jean Segura’s groundout plated Hart with the final run of the inning.
The Brewers added a run in the eighth on Braun’s sacrifice fly.
The Brewers took a 2-0 lead in the fourth. Braun led off with a fly ball to straightaway center and when Bryce Harper lost the ball in the sun, it dropped in and Braun ended up on second with a double.
After Ramirez flied out, Hart singled to left. Braun had to hold up initially and stopped at third. Lucroy then grounded a single just past a diving Adam LaRoche to make it 1-0. Logan Schafer doubled to the wall in right, scoring Hart to make it 2-0.
Nationals starter Chien-Ming Wang, making his first start since June 19, went four innings and gave up two runs on eight hits while striking out two.
Wang was starting because Tuesday’s rainout and Wednesday’s doubleheader meant Sunday’s scheduled starter, Jordan Zimmermann, would have been working on three days’ rest. Johnson chose to push Zimmerman back a day rather than pitch him on short rest, and gave the start to Wang.
The Nationals tied it in the fifth. Desmond led off with a walk and Danny Espinosa followed with a double to left, sending Desmond to third.
Milwaukee starter Yovani Gallardo fanned Kurt Suzuki with a 3-2 fastball and quickly got ahead of pinch hitter Chad Tracy 0-2. Tracy worked the count to 2-2 and fouled off two more pitches before lofting a single to short right, scoring Desmond while Espinosa stopped at third.
The next batter, Werth, tied the game with a sacrifice fly to left.
Gallardo entered the game having won his last eight decisions. He went five innings, allowing two earned runs and six hits. He walked two and struck out five. The Brewers have won Gallardo’s last 11 starts.
Twice in the first three innings, the Nationals had runners on first and third with one out against Gallardo and didn’t score.
LaRoche led off the second with a smash that deflected off first baseman Hart’s glove down the right-field line for a double. One out later Desmond hit a slow roller to third and beat the throw, putting runners on the corners. Espinosa hit a hard liner, but Hart caught it and stepped on the bag to double up Desmond.
With one out in the third, Wang doubled to left center. Werth singled to right, moving Wang to third, but Harper hit into a 6-4-3 double play.