Rodriguez connected for a run-scoring single in the third inning and added a two-run hit in the fourth, helping lead New York to its ninth victory of the spring. Rodriguez is coming back from an injury-marred 2011 season that limited him to just 99 games.
Right-hander Michael Pineda made his fourth spring start for New York, permitting two runs -- both on Andrew McCutchen's first-inning homer -- and three hits in three innings. Pineda settled in after early command problems, walking one and striking out five.
"You don't see that a lot from young pitchers," Yankees manager Joe Girardi said of Pineda. "Sometimes, they struggle to make an adjustment, and he made it pretty quick. He has got a pretty good sense of what he needs to do."
McCutchen's homer came with Jose Tabata aboard and was his second of the spring. Erik Bedard was charged with four runs and five hits in 3 2/3 innings, walking three and striking out three in his third Grapefruit League start.
"I'm glad he got a chance to get his pitch count up, and he had some very clean sequences," Pirates manager Clint Hurdle said of Bedard, who retired the side in order in the second. "He got to throw all his pitches and to work on his slide-step, so I thought it was a good outing for him."
Mariano Rivera threw eight of his nine pitches for strikes during a scoreless fourth inning for New York and has yet to allow a hit this spring.
"He looks really sharp," Girardi said of Rivera. "We're really pleased with where he's at."
Yankees right fielder Nick Swisher was lifted for a pinch-runner in the third inning after experiencing tightness in his right groin; Swisher's replacement, Justin Maxwell, laced a two-run double in the fifth.
Curtis Granderson reached in all four of his plate appearances, drawing two walks and hitting a single and a double.
Up next: Rodriguez, Robinson Cano, Mark Teixeira and the rest of the Yankees will hit the highway early on Wednesday, traveling to meet the Rays for a 1:05 p.m. ET game in Port Charlotte, Fla., that will air on MLB.TV. Right-hander Phil Hughes will make his second start and fourth appearance of the spring, opposite former Bombers pitcher Kyle Farnsworth.