Rodriguez, the designated hitter in two earlier games, hit a pop-fly double and struck out in five innings. He made a nice, backhanded grab on Tyler Moore's grounder and threw him out to end the third.
Yankees manager Joe Girardi and general manager Brian Cashman say Chase Headley will be their starting third baseman. Rodriguez will compete primarily for at-bats at DH as he returns from a one-year drug suspension. He is also going to get limited time at third and possibly first base.
"Game speed is the one thing you can't emulate," Rodriguez said. "Being away from the game, that's the hardest thing to adjust to. I'll give it a shot."
The three-time AL MVP, who turns 40 in July, has not played a full season since 2007 because the suspension, operations on both hips and other injuries.
"We understand he's not 25 years old, but I haven't seen a difference from where he was a couple years ago," Girardi said.
Washington starter Doug Fister allowed one hit in two scoreless innings.
"I feel healthy and that's my first and No. 1 key," Fister said. "Not a bad outing to look at overall. Seeing some of the swings, seeing some of the locations, I feel OK where we're at right now."
Michael Taylor homered on the first pitch of the game against Adam Warren and Tyler Moore doubled twice for the Nationals.
"Went up there aggressive and got a good pitch to hit," Taylor said. "I think that's something I do naturally, sometimes a little too aggressive. I think that's part of my game."
Nationals: Gio Gonzalez is scheduled to make his first start Monday against Atlanta.
Yankees: Michael Pineda will face Tampa Bay in his first start Monday. Nathan Eovaldi will also pitch. ... Masahiro Tanaka will make his first start Thursday night against Atlanta. The Japanese ace missed 2 1/2 months last year while rehabilitating a partially torn ulnar lateral ligament in his right elbow.
Yankees: CC Sabathia, hobbled by a degenerative cartilage problem in his right knee last year that required season-ending surgery in July, broke Greg Bird's bat in half on his 29th and final pitch in batting practice. "Feels great," Sabathia said. "No swelling. No need to ice afterwards." Sabathia will pitch in a simulated game later this week .... INF Brendan Ryan (strained back) is hopeful of doing on-field drills for the first time in a few days.
Yankees: Warren gave up one run and four hits over three scoreless innings in his second start.
Nationals: Fister got five of his six outs on grounders, including Carlos Beltran's double play in the first.
Yankees spring training instructor Reggie Jackson went into the stands to give an autographed baseball to a fan struck by a bat that Washington's Jose Lobaton lost control of during a swing in the second.