The Hurricanes (2-0) scored 48 points in the second half as Rodriguez took over. The former Kansas State guard hit three consecutive 3-pointers that helped Miami take the lead with 1:45 left. His free throw tied it with 1:13 remaining. But his fifth 3 of the game was the dagger that ended Florida's school-record, 33-game winning streak at home.
Kasey Hill had a hand in his face and even knocked him to the floor, but the off-balanced shot went in.
Florida (1-1) had a final chance to send it to overtime, but Michael Frazier II missed a jumper at the buzzer.
Eli Carter led the Gators with 21 points, including 16 in the second half.
Carter hit a driving layup with a minute to play that put Florida back ahead 67-65, but Rodriguez answered on the other end. Carter had a chance to respond, but he was called for a charge in the lane with 3 seconds to play.
Florida was down four players in the game, including starting forward Dorian Finney-Smith.
Finney-Smith missed the game because of two hairline fractures in the index and middle fingers on his left, non-shooting hand. Finney-Smith had been cleared to play Monday, but his hand swelled when casted and became really painful.
Florida also was without forward Chris Walker, forward Alex Murphy and guard Dillon Graham. Walker served a two-game suspension to start the season. Murphy has to six out eight more games under NCAA transfer rules. And Graham left the team Saturday and intends to transfer.
The short-handed Gators started walk-on Jacob Kurtz, who finished with six points and eight rebounds.
Florida's real problem was its second-half defense. Coach Billy Donovan ripped his team last week because of shaky defense, saying the Gators weren't "remotely close" to deserving their lofty ranking.
It showed Monday. The Hurricanes shot 65 percent in the second half and 70 percent from 3-point range.
Miami: The Hurricanes played at Florida for the first time since losing in the 2009 NIT. They improved to 7-29 all-time against the Gators in Gainesville, including 2-1 during Florida coach Billy Donovan's 19-year tenure. ... Miami's Jim Larranaga faced Florida as George Mason's coach in the 2006 Final Four.
Florida: The Gators will play the back end of the home-and-home series in Miami next year. ... Former Florida players Teddy Dupay and Major Parker were on hand for the game.
Miami plays Drexel in the Gildan Charleston Classic on Thursday
Florida hosts Louisiana-Monroe on Friday