Overbay had an RBI double Thursday as the Yankees ended their Florida segment of spring training with a 2-1 loss to the Pittsburgh Pirates.
New York general manager Brian Cashman said Overbay, signed to a minor league contract Tuesday hours after being released by Boston, had the inside track for the job with Mark Teixeira on the disabled list because of a wrist injury.
"It's kind of been a whirlwind," Overbay said.
Overbay's wife made a round trip drive Thursday to Fort Myers -- around 120 miles each way -- to get his stuff for the Yankees postgame charter flight.
The Yankees released Juan Rivera, who played extensively at first during the exhibition season.
"Overbay, and what he's done in his career and playing first base, we were just a little more comfortable," New York manager Joe Girardi said.
Teixeira is out until at least May with a wrist injury.
Pirates fifth starter Jeff Locke gave up four hits and had three strikeouts in six scoreless innings.
"I would say the biggest thing for me today is a confidence-builder," Locke said. "It's easy to feel good about today's outing, especially when it's the last one. I'm excited, ready to get roaring."
"I felt like I got ahead of hitters better today than I had in the outings prior," Locke said. "I was able to throw my changeup much more today. That felt good. Curveball felt good. But the combination from fastball to changeup was what made today the best."
Yankees starter Hiroki Kuroda allowed one hit over six shutout innings.
Kuroda retired 10 in a row before Garrett Jones' third-inning infield single, which deflected off the right-hander's glove. He then got his final eight batters out.
"The main thing was to stay healthy rather than thinking about the mechanics, and I was able to do that," Kuroda said through an translator about his exhibition season.
"It's part of the game," New York closer Mariano Rivera said. "No one likes to get hurt, but it happens. What we need to do is just make sure that we play the game the way we know how to play. Do the little things. Pitch. We win games like that. Someone will step up. Someone will do what needs to get done to win games."
New York's regular-season opener Monday against Boston at Yankee Stadium will be the final one as a player for Rivera, who announced his retirement after this season on March 9.
There is no timetable for when Jeter, who will stay in Florida, will return. The Yankees are hopeful that Granderson (forearm) could play in May, while Rodriguez (hip) might comeback in July.
"Hopefully we'll go through our injury problems in February, March and April, and after that be as healthy as possible," Youkilis said.
Yankees second baseman Robinson Cano went 1 for 3 after missing Wednesday night's game against Baltimore due to a stomach virus.
"I feel good today," Cano said.
New York closes out the exhibition season with games at Washington on Friday and against Army Saturday at West Point. The Pirates are off Friday before playing their Double-A affiliate Altoona on Saturday.
Ben Francisco and Brennan Boesch are the frontrunners for the two Yankees' backup outfield positions. ... LHP Andy Pettitte and Rivera are scheduled to pitch in Friday's exhibition game against the Nationals. ... Teixeira will have his injured right wrist re-examined Monday. ... New York INF Ronnier Mustelier has a bruised right knee and will remain at the Yankees' complex in Florida.