With the score tied at 3 and reliever Jordan Norberto on the mound, Desmond singled to right field to drive in Adam Kennedy and give Washington a one-run lead. Ryan Zimmerman added a home run in the eighth for insurance.
Right-hander Stephen Strasburg started the game for the Nationals and was much better than he was on Tuesday, when he allowed six runs in 4 1/3 innings against the Marlins. On Sunday, Strasburg lasted five innings and allowed three runs -- one of which was earned.
"I was talking to Stephen a little bit ago. He said that it is the best he felt," manager Jim Riggleman said. "The ball was coming out of his hand good. Stras did a great job and gave us a chance to win."
After an easy first inning, Strasburg struggled in the second. He allowed a leadoff homer to Adam LaRoche. With one out, after Mark Reynolds singled, Stephen Drew followed and hit a comebacker to Strasburg, who threw the ball away after trying to throw out Drew at first base.
Reynolds scored all the way from first base, while Drew ran all the way to third on the play.
"Instead of fielding with my glove, I barehanded the ball," Strasburg said. "Then I realized after that, I had a lot more time. I tried to throw a little bit slower. It just sailed on me. It was pretty much bad fundamentals all around. I know what I did wrong. If it comes again, I know I'm going to do it right."
Drew would later score on a sacrifice fly by Gerardo Parra.
"He throws hard," D-backs second baseman Kelly Johnson said about Strasburg. "Velocity can help a lot of things. I saw three good pitches -- fastball got up on you quick. I think he probably didn't command his fastball as well as normal, but then he had pretty decent command of the breaking ball, and his changeup was one of those, 'there it is, there it isn't.'"
After that second inning, Strasburg retired eight out of the next 11 hitters he faced.
"I thought I made a lot of improvements," Strasburg said. "I started to get the feeling back. I was able to locate my pitches a lot better today. It was a good win. I thought I made a lot of improvements. I started to get the feeling back. I was able to locate my pitches a lot better today. It was good to go out there after a tough day yesterday and win the series."
Strasburg could have gone longer than the five innings, but a two-minute delay because of protesters on the field prevented that from happening.
"I was going to let him go back out there and pitch," Riggleman said. "We are in that gray area -- 85 pitches. I had the 95-pitch limit. Maybe we would have gone to 100 today, but once [the protest] happened on the field, it took a little while. It was undecided as to whether I wanted to let him go back out there anyway. Once we sat in there a little bit longer with the stuff going on, I just decided that I was not going to send him back out there."
After Strasburg grounded out in the top of the fifth inning, the protesters were on the field because they wanted the 2011 All-Star Game to be moved out of Arizona because of recent immigration legislation.
"It looked like it was choreographed a little bit," said reliever Tyler Clippard, who won his team-leading ninth game of the season. "One guy ran out. He was trying to deek out the security guys, and then a couple of more people came out on the field.
"It is unfortunate. It's kind of ridiculous to me if people feel like a baseball game is grounds to kind of do a protest or whatever they were trying to do. I'm not really sure. It's really not the smartest thing to do. They are probably sitting in a jail cell right now, and they really didn't accomplish anything."
But the Nationals would accomplish a lot on Sunday. They tied the score by the fourth inning off D-backs starter Barry Enright. In the second inning, Josh Willingham scored on a single by Ivan Rodriguez. In the fourth, Willingham tied the score on a two-run homer. It was Willingham's first home run since July 2 against the Mets. It took 112 at-bats before hitting his 16th home run of the season.
"I have to say that is my longest drought," Willingham said. "I try not to think about. But I knew it was a long time since I hit a home run. You kind of wonder if you could still hit one."
The bullpen took over and shut out the D-backs for four innings, with Drew Storen picking up his second save of the season.
With the victory, the Nationals improved to 51-67, and they won their first series since late July against the Phillies.
"We needed to win a series," Willingham said. "It has been a while. So we hope to keep that going in Atlanta."