Rodriguez achieved a unanimous victory after coming out on top on all three judges' scorecards by convincing margins of 120-106, 120-106 and 118-108.
Butler, who held the same title briefly in 2014, was unable to win it back this time after failing to make the weight on Friday.
The belt was at stake for Rodriguez only after Butler came in above the bantamweight at 8st 9.3lbs.
Butler was given two hours, per IBF rules, to shift the weight, but he didn't come back to the scales.
The fight still went ahead but Rodriguez dropped Butler twice in the first round.
"I found it easier than I should have done, but a win's a win," Rodriguez told the BBC.
Meanwhile, Butler said: "The weight was a mistake on my behalf and it won't happen again. You live and learn."