The Bulldogs won for the sixth time in seven games, clinched the Southeastern Conference Western Division title and damaged the two-time defending national champion's chances of making a 10th consecutive NCAA tournament.
Mississippi State (20-8, 11-3), which reached 20 wins for the seventh time in the last decade, dominated Florida in the low post.
After trailing by 13 points late in the first half, the Gators (21-8, 8-6) trimmed the lead to 41-35 just after halftime.
But then Rhodes and Jarvis Varnado took over. Hansbrough came up big, too.
Rhodes made three baskets inside, Hansbrough hit a 3-pointer and Varnado blocked two shots to help the Bulldogs push the lead back to 13.
Varnado, the nation's leading shot blocker, finished with 11 points, 11 rebounds and seven rejections.
Marreese Speights led Florida with 20 points and 10 rebounds, but the sophomore center also missed a dunk and two easy lay-ups that could have helped keep it close. Nick Calathes added 18 points, seven rebounds and four assists.
The Gators cut the double-digit lead to 58-52 on Speights' putback with about 3 minutes remaining, but Hansbrough hit his fourth 3 of the game to stretch it back out for good.
Florida, which has lost five of eight, probably needs to beat top-ranked Tennessee on Wednesday and win at Kentucky to make the tournament. The Gators also could get in by winning the SEC tournament -- hardly probable the way they've played down the stretch.
Mississippi State used four 3-pointers and two three-point plays in the first 13 minutes of the game to build a double-digit lead, 26-16.
Hansbrough did part of the damage, hitting two open 3s and driving for another score as Florida crashed inside on Mississippi State's big men.
Rhodes and Varnado did their part, too. Rhodes had six points in the first half and Varnado added seven points, eight rebounds and three blocks.
The Gators settled for outside shots early, but then decided to test the country's leading shot blocker.
It wasn't a smart decision.
In the end, the undersized Gators lost another game because they didn't shoot very well. They shot 36 percent from the floor and were 7-of-25 from 3-point range.
The Bulldogs, working inside-out most of the game, shot 42 percent from the field.