A-Rod was not made available to the media following the shortened game.
Thursday marked the halfway point of Rodriguez's 20-day rehab process as he continues to recover from offseason surgery on his left hip.
Teammate Derek Jeter made his return to the Yankees on Thursday as the designated hitter, going 1-for-4 with an RBI before departing New York's 8-4 win over Kansas City with a tight right quad.
While Jeter was back with the Yankees before his rehab clock ran out, Yankees general manager Brian Cashman said on Thursday that Rodriguez "would go the whole 20 days" before returning to the Yankees.
"There's a reason he's in A ball, and there's a reason we were able to put Derek in Triple-A right from the start -- because Derek was obviously much farther along than where Alex was," Cashman said.
Before Thursday, neither of the two components that make up the left side of the Yankees' infield had played since last season.
Rodriguez may play for Tampa on Friday. He initially planned to take Friday off, potentially to attend a reported meeting with Major League Baseball regarding his possible involvement with the former Biogenesis clinic in South Florida.