FORT MYERS, Fla. -- Aaron Cook is headed to the minors. If he keeps pitching the way he did Monday, he might not stay there long.

Cook threw five solid innings, Adrian Gonzalez had two hits and the Boston Red Sox beat the Washington Nationals 4-2.

Cook allowed only two hits, including Danny Espinosa's leadoff homer in the fourth. He struck out two, walked one and finished the spring with a 1.88 ERA.

Boston signed the veteran right-hander to a minor league contract in the offseason to provide pitching depth and another option at the back of the rotation.

The Red Sox were cautious with Cook early in the spring because of past health issues. His outing Monday surprised manager Bobby Valentine.

"Coming in I did not expect him to be giving us five pretty good innings the last day of spring training," Valentine said. "So it's a very pleasant development. I thought his sinker was really good today. And it's great to have that kind of depth in our starting rotation. I think a few handful of outings like that where he builds up his pitch count and maintains his strength will be a pleasant happenstance."

Cook is slated to go to Triple-A Pawtucket and work as a starter there.

"There's always disappointment when they tell you you're going down, but I took it all in stride," Cook said. "I knew the situation when I signed here. And I'm just going to go out there and be the same pitcher whether it's at Boston, Pawtucket, no matter where I'm at. I'm going to go out there, try to get groundball outs, and be very efficient."

Franklin Morales worked a perfect ninth for the save.

Jordan Zimmermann tossed five innings for the Nationals in his final exhibition tuneup, allowing six hits and three runs -- two earned. He dropped to 1-2 with a 3.38 ERA in spring training but was satisfied with his outing.

"Yeah, I'm definitely ready," Zimmermann said. "I felt pretty good today. Missed a few balls, made a few bad pitches and I mean, these guys are some good hitters. Adrian Gonzalez is probably one of the best hitters in the league and he showed it again today. I mean, I threw him the kitchen sink and he still got two hits and a walk. Overall I feel good and I'm ready to get going."

Nationals manager Davey Johnson also was pleased with Zimmermann's performance.

"I liked the way Zim threw the ball," Johnson said. "That was a good tuneup for him. Good work day."

Tyler Clippard and Brad Lidge each worked a scoreless inning out of the Nationals bullpen.

Washington outfielder Roger Bernadina left in the first inning with a bruised right knee. He reached base on Gonzalez's error at first and advanced when Cook's pickoff attempt hit him in the knee. After reaching second, Bernadina was replaced by pinch-runner Brett Carroll.

"I delayed going out there because I wanted him to play," Johnson said. "When I asked, `Are you OK?' I didn't get much of a response. Hopefully it's nothing serious. He'll be ready to go tomorrow because I want to get him playing a couple days."

Chad Tracy had two of the Nationals' five hits.

The teams meet again for another exhibition game Tuesday in Washington.

Game notes
Nationals infielder Steve Lombardozzi and outfielders Tracy, Carroll and Xavier Nady have all won spots on the opening-day roster. Washington outfielders Michael Morse and Rick Ankiel, along with closer Drew Storen and right-hander Chien-Ming Wang, will begin the season on the disabled list. ... Gonzalez raised his spring training average to .357. ... Injured Red Sox players who will stay behind in Fort Myers to continue working out and rehabbing at the team's training complex include pitchers Rich Hill, Daisuke Matsuzaka, Andrew Miller, John Lackey, Chris Carpenter and Bobby Jenks, left fielder Carl Crawford and outfielder Ryan Kalish.