"Alex has been playing great. He's getting on base, and he's doing everything that you want," Girardi said. "So I just flip-flopped them for now. Alex is swinging great.
"It's just watching his at-bats, as you continue to watch his at-bats. He's taking his walks, and he's being patient. He's doing just a lot of things right, and that's why I moved him up."
Beltran, who sat out the last two games with a head cold, had hit third in each of his nine starts this season. The 37-year-old outfielder entered Monday night batting .184/.238/.289 with nine strikeouts and three walks.
"Just getting comfortable at the beginning of a season, I think. You see a lot of really good hitters start off slow. You just kind of ride through it," Girardi said. "You know eventually it's going to change and they're going to get back to where they're supposed to.
"It's unfortunate he got sick. I thought he was swinging the bat better. I think it was hard to ignore what Alex was doing."
What Rodriguez did was hit .316/.447/.711 in his first 12 games. He leads the Yankees with four home runs, 11 RBIs, 10 runs and nine walks, entering Monday.
"You look at the run production that we've gotten from him, a lot of our wins are directly the result of what he's done in certain games," Girardi said.
Adam Berry is a reporter for MLB.com. Follow him on Twitter at @adamdberry. This story was not subject to the approval of Major League Baseball or its clubs.