Robertson hit his first batter, Danny Espinosa, then induced a double-play grounder by Tyler Moore to shortstop Derek Jeter, who fielded a tough-hop grounder. Robertson is replacing career saves leader Mariano Rivera, who retired after last season.
"It was OK. ... I got three outs," Robertson said. "I would have liked to throw some better pitches, but I'll get another chance."
Jeter went 0 for 3, including a double-play grounder. He is hitless in seven at-bats over three spring training games. The Yankees captain broke an ankle in the 2012 AL championship series and played in just 17 games last season.
Zach Walters hit a solo homer for the Nationals.
Nationals: Outfielder Bryce Harper, sent home Sunday with flulike symptoms, is expected to play Tuesday against Atlanta.
"He actually wanted to come on the trip, but after yesterday I just told him to take another day," manager Matt Williams said.
Right fielder Jayson Werth, who strained his right biceps while working out Saturday, will be evaluated Tuesday.
Yankees: First baseman Mark Teixeira, limited to 15 games last year because of a right wrist injury, hit against pitchers for the first time this year and hopes to play Thursday.
Teixeira went 2 for 4 batting right-handed in a simulated game, including a lined single and a bloop single to right that he jokingly called a triple.
"First of about 20 this year," he said.
Teixeira, a switch-hitter, also hit two foul balls and missed a pitch during 12 pitches left-handed.
Manager Joe Girardi didn't rule out outfielder/designated hitter Alfonso Soriano (flulike symptoms) from also playing for the first time Thursday.
Washington right-hander Stephen Strasburg is scheduled to make his first start Tuesday.
Strasburg, who had bone chips removed from his surgically repaired right elbow last October, is to throw two innings. The 25-year-old is 29-19 over four seasons, including 8-9 last year with a 3.00 ERA in 30 starts.
"We're not going to push him to three at this point regardless of his pitch count," Williams said.
Nationals: Fifth starter candidate Ross Detwiler gave up four runs, five hits and struck out three in 1 1/3 innings.
Tanner Roark, also in the mix for the final rotation spot, scattered two hits over two scoreless innings.
Yankees: Ivan Nova threw three hitless innings, striking out four.
Yankees spring training instructor Andy Pettitte arrived for a three-day stay and said he plans to stay retired.
Pettitte, who threw batting practice, retired after the 2010 season, returned for 2012 and 2013, then retired again.
"There's nothing in the works," he said.
Pettitte, 41, discussed the announcement last month that Jeter intends to retire after this season. The Yankees captain turns 40 in June.
"I think he'll down play it, of course," Pettitte said. "I don't think he likes a lot of attention. He needs to be honored. I think he's going to have a great year, if he's healthy."
Hall of Fame quarterback Joe Namath was an honorary co-manager for the Yankees. Wearing No. 12, he sat next to Girardi for part of the game.
"It's special," Namath said. "This has been excitement from the get-go. I'm a baseball fan. I'm a Yankee fan. I'm a people fan."
New York Jets coach Rex Ryan also was at the game.