Morse hit a tying, two-run homer in the ninth inning, then delivered a two-run double in the 11th that sent the Nationals over the Brewers 11-10 on Sunday.
"It's crazy because you never know what this game has in store until the last out," Morse said. "We fought and kept fighting and they kept fighting, too. It was a great game."
Morse's homer with one out in the ninth off John Axford made it 9-all. The opposite-field shot barely made it over the wall in right.
"It seemed like it was a boxing match," Morse said. "It kept going back and forth, back and forth. We just hung in there and came through on top."
The NL East-leading Nationals rallied for four runs in the eighth to tie it at 7.
The Brewers have lost nine of 10. Milwaukee's duo of Francisco Rodriguez and Axford each allowed three runs in failing to protect another late lead.
"It's just the way it's going with the bullpen," Milwaukee manager Ron Roenicke said.
Craig Stammen (4-1) pitched 2 1/3 hitless innings for the victory.
"I felt like I really let the team down there today," Mattheus said. "It was a huge weight lifted off my shoulders when he came through and got a big hit. It doesn't make what I did OK, but he picked me up and really came through in the clutch."
Milwaukee opened a 7-3 lead on Weeks' 11th home run of the year in the seventh, but Rodriguez gave up three runs in the eighth and was removed for Axford. Corey Brown then scored the tying run on a wild pitch in the dirt from Axford that went to the backstop.
Aoki and Gomez hit back to back solo home runs in the bottom of the eighth to give the Brewers a 9-7 lead.
Axford struck out Zimmerman to open the ninth. He then walked Mark DeRosa before giving up the home run to Morse, his eighth of the year.
Milwaukee starter Mark Rogers, starting in place of the traded Zack Greinke, pitched 5 2/3 solid innings in his first major-league appearance since 2010. The right-hander was the fifth pick in the June 2004 amateur draft, but had pitched only 10 innings in the majors before replacing Greinke in the Brewers' rotation.
Rogers gave up a home run to Steve Lombardozzi to lead off the game, but settled in to keep the Nationals off-balance. He gave up two runs on six hits and struck out seven.
The Brewers managed only five hits in six innings off Washington starter Gio Gonzalez, but took advantage of the All-Star's wildness. Two batters who walked and another who was hit by a pitch scored, and the Brewers also scored on a bases-loaded walk.
A play in the sixth inning resulted in three of the four umpires involved in separate arguments at the same time.
The Brewers led 3-2 and had the bases loaded with one out when Aoki laid down a squeeze bunt. Gonzalez made a quick, off-target throw to first that forced Lombardozzi to stretch into foul territory and make the catch while Milwaukee's Jonathan Lucroy easily scored from third.
First base umpire Tim Welke ruled Aoki safe, and Lombardozzi immediately began to argue while holding the ball in his glove. Seeing the argument, Cody Ransom then sprinted home. Home plate umpire Mike Estabrook, however, ruled time had been called and sent Ransom back to third.
Milwaukee manager Ron Roenicke came out and argued with Estabrook that time had not been called. Washington manager Davey Johnson and Lombardozzi were arguing with Welke at first at the same time while Ransom was complaining to third base umpire Laz Diaz.
Paul Schrieber at second base was the only umpire not in an argument.
Greinke was traded to the Los Angeles Angels on Friday and made his first start for his new team on Sunday. He took the loss against the Rays. ... Washington 1B Adam LaRoche was removed from the game in the fourth inning due to tightness in his back. He is day to day and Johnson said he thought LaRoche would be available for the team's next game. ... Before the game, the Brewers traded C George Kottaras to the Oakland Athletics for RHP Fautino De Los Santos. He was optioned to Triple-A Nashville. The Brewers also optioned RHP Tyler Thornburg to Nashville after the game. ... Aramis Ramirez was held out of Milwaukee's starting lineup to rest his sore left wrist. He pinch hit in the sixth and was intentionally walked. ... Harper returned to the lineup after missing Saturday's game with a stomach virus. ... Before the game, Washington unconditionally released OF-1B Xavier Nady.