Beltran gave the Yankees the lead in the seventh inning with a two-run shot to left off Mike Dunn, one frame after Gardner tied the game with a two-run shot to right off Marlins starter Mat Latos.
Rodriguez notched an RBI single in the first and another single in the fifth, needing one more to become the 29th Major Leaguer to reach the milestone. He lined out hard to right field in the sixth against Dunn and walked on four pitches, all inside, from Sam Dyson in the eighth.
Giancarlo Stanton hit a sixth-inning homer off Yankees starter CC Sabathia, who permitted three runs over six innings in a no-decision.