Desmond, who had 22 home runs entering Saturday, stole his 20th base in the fourth inning against right-hander Zach Wheeler. After he reached third, Desmond scored on a throwing error by catcher Travis d'Arnaud.
Desmond downplayed his accomplishment.
"This is something I'm not going talk too much about," Desmond said about the 20/20 milestone. "I'm really happy where we are at as a team. We are playing pretty good baseball. It's just an exciting time of the year for everybody.
"Individual stuff has never exited me. Like I said, I'm really happy that we are playing really good baseball. We kind of extended the lead in our division. We are putting ourselves in a good position to get to the postseason."
Desmond swiped his 21st base after hitting a two-run single in the Nationals' three-run fifth that helped them trim their magic number to win the NL East to six games.
Bill Ladson is a reporter for MLB.com and writes an MLBlog, All Nats All the time. He also could be found on Twitter @WashingNats. This story was not subject to the approval of Major League Baseball or its clubs.