WASHINGTON -- Every now and then, Chris Davis breaks free from his agonizing season to send out a reminder of just how dangerous he can be at the plate.
Anthony Rendon homered for the Nationals, who lost for only the second time in nine games.
After Cruz led off the 11th with a broken-bat single off Craig Stammen (0-4), Davis worked the count full before launching a drive into the center-field seats to end a 2-for-38 funk that had dropped his batting average to .198.
''When we stopped them the inning before, I knew the next inning I was coming up,'' Davis said. ''And with Nelson being as hot as he is, I just kind of thought, `This is my chance to redeem myself.' I've been doing everything I can. I want to be the player I know I can be for these guys. I know it will be huge for this team if I can step up and start swinging a little bit. So it was definitely good to come through right there.''
It was his 14th home run of the season, the first since a game-winning, pinch-hit shot against the Chicago White Sox on June 23. Davis led the majors with 53 homers last year.
''Really happy for Chris,'' Orioles manager Buck Showalter said. ''He's been beating himself up pretty good. Anybody out there doesn't have to do it because he's doing it enough on his own. I think everybody on the club really felt good for him, to have that big knock there.''
No one felt better than Davis himself.
''Nobody likes to struggle, but at the same time I try to keep a positive mind frame,'' he said. ''If you sit there and dwell on how bad you are scuffling it's going to be hard to get out of it.''
''I really did not think he would be able to hit that pitch out,'' Stammen said of the pitch to Davis. ''He was right on it and he was looking for it. It was a little bit higher than I wanted.''
T.J. MacFarland (2-2) worked two scoreless innings for the win.
Tillman gave up two runs on five hits, striking out six and walking one.
Strasburg struck out nine and allowed two runs on four hits, three by Machado. The nine strikeouts were his most in six starts since June 4.
''I just wanted to go out there and try to build out the last start, just focus on the execution of the pitches,'' the right-hander said. ''We played great defense, but it was tough how it ended.''
Each team managed only one hit over the first three innings. Machado doubled with one out in the top of the first, and Strasburg singled on a 3-2 pitch in the third.
In the fourth, Machado led off with a single and Cruz drove a 1-0 pitch over the wall in right-center. Cruz has already topped his home run total of last year, when he hit 27 during a season cut short by a 50-game suspension as part of the Biogenesis performance-enhancing drug scandal.
Strasburg struck out the next four batters before Tillman grounded out to end the fifth.
The Nationals didn't get a runner past first base until the sixth, when Denard Span hit a leadoff single and Rendon followed with his 13th home run, the first since June 24. He hit only seven last year.
Washington's Bryce Harper went 0 for 3 and is 4 for 24 since coming off the DL on June 30. ... The Orioles optioned RHP Kevin Gausman to Triple-A Norfolk and purchased the contract of RHP Julio DePaula from Double-A Bowie. Showalter said the move was designed to fortify the bullpen while addressing the inning-count Gausman is on this year. ... Nationals RHP Doug Fister and Orioles RHP Bud Norris each seek their eighth win Tuesday night. ... Washington played its 12th consecutive errorless game. Since moving from Montreal in 2005, the Nationals' longest errorless streak is 13 games, in 2011.