Luis García homered early for the Nationals, who are last in the NL East.
With right-hander Thyago Vieira (0-1) on for his second inning of relief in the 11th, automatic runner CJ Abrams advanced to third base on Lane Thomas’ flyout and scored on Meneses’ third sacrifice fly of the season.
With runners at the corners in the bottom half, Robert Garcia (1-2) got pinch-hitter Rowdy Tellez to ground into a game-ending double play to secure his first major league win.
“He smoked the ball, and it was a great play by the first baseman,” Brewers manager Craig Counsell said. “Tip your cap to that, that was a great play. Then he made a great play to throw home as well, not throw to second.”
Michael Chavis took over at first after being inserted as a pinch runner for starting first baseman Dominic Smith in the ninth.
Nationals manager Dave Martinez said he has confidence in Chavis to make the big play.
“We can't do that unless we know that Chavis takes his work over at first base and those ground balls,” Martinez said. “Those are the things that he does. So, we were able to pinch run for Dom knowing that he can go over there and play first base and play it well. He's done it in his career. For me, it was a no-brainer.”
Garcia also pitched out of trouble in the 10th, holding the Brewers scoreless after they loaded the bases with one out.
Milwaukee had runners at second and third with two outs in the ninth before Kyle Finnegan struck out Andruw Monasterio.
The Nationals had a chance to take the lead in the eighth. But with runners at the corners, Andrew Chafin entered and threw one pitch, getting the speedy Abrams to ground into an inning-ending double play.
“That was a tough spot,” Counsell said. “Abrams is a very difficult player to double up. We caught a break, hit a groundball at somebody, we were playing in and we were able to turn it.”
Hunter Harvey took over for Nationals starter Patrick Corbin and retired the side in order in the seventh and eighth.
Corbin allowed three hits over five scoreless innings before the Brewers manufactured a run in the sixth to tie the game. Mark Canha singled, stole second, advanced on a sacrifice and scored on Carlos Santana’s sacrifice fly.
“Good to see us come away with this win,” Corbin said. “Just credit to the bullpen. They've been pitching a lot for us and pitching well. Good to see them finish it out.”
García homered in the second to snap a shutout streak of 22 2/3 innings for Milwaukee starter Brandon Woodruff.
García contributed a nice running catch with his back to the infield in the first. He singled and stole second in the fifth.
Woodruff allowed three hits - two by García - over six innings and struck out six.
Brewers OF Christian Yelich, who had missed six straight games with a sore lower back before returning Friday night, was out of the starting lineup for the second consecutive game.
The Nationals were 0 for 9 with runners in scoring position. The Brewers went 1 for 11.
Nationals: Recalled RHP Cory Abbott from Triple-A Rochester and optioned RHP Amos Willingham to the same affiliate. It is Abbott’s fourth major league stint this season.
Brewers: Reinstated OF Blake Perkins (left oblique) from the 10-day injured list and optioned OF Joey Wiemer to Triple-A Nashville.
Nationals: RHP Joan Adon (2-2, 5.92 ERA) faces RHP Mike Clevinger (7-8, 3.61) and the Chicago White Sox in the opener of the Nationals’ final homestand of the season.
Brewers: RHP Freddy Peralta (12-8, 3.79 ERA) opposes RHP Adam Wainwright (4-11, 7.95) and the St. Louis Cardinals in the opener of a four-game road series.
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