Alabama had a chance to tie in the final seconds, but Trevor Lacey's 3-pointer bounced off the front of the rim.
Though the game was usually tight, the Crimson Tide never led.
"I think this time of year, you've got to find ways to advance and move on and we did," Florida coach Billy Donovan said.
Florida (23-9) will face top-ranked Kentucky on Saturday in the semifinals. The Gators lost to the Wildcats twice this season, but hope their postseason-tested team will be up for the challenge. Much of Florida's roster was around last season, when the Gators advanced to the Elite Eight.
"Our team, we're mature," said senior guard Kenny Boynton, who hit two late free throws to seal the victory. "We've been through everything, played the best teams throughout this year, so I think we'll come out tomorrow and be ready to play."
Alabama (21-11) lost for just the second time in seven games. Green had 22 points, Trevor Releford scored 12 and Lacey added 11.
"My teammates did a great job of finding me," Green said. "I think we did a great job of just passing the ball and playing as a team."
And this one wasn't much different -- except for the final result. The Gators shot just 32 percent (8 of 25) from the field in the first half and led 26-24 at the break after Alabama's Levi Randolph hit a long 3-pointer at the buzzer.
Alabama's defense had something to do with Florida's offensive woes. The Crimson Tide's bruising, grind-it-out style is completely opposite of the Gators, who like to run, shoot and turn the game into a constant sprint.
It wasn't until Erving Walker's outburst early in the second half that the Gators were finally able to get some separation. The 5-foot-8 point guard scored seven points in less than five minutes, shrugging off Alabama's physical guards and consistently getting into the lane, where he could finish at the rim or find another shooter around the 3-point line.
For a while, it looked as if the Gators looked would cruise, but Alabama erased a 12-point deficit in less than six minutes. The Tide got a huge game from Green, who was 7 for 14 from the field and 8 of 9 from the free-throw line. He also grabbed 10 rebounds and dished out four assists.
But that one miss at the free-throw line hurt.
Green had a chance to tie it with 20.3 seconds remaining, but his second of two foul shots rattled out and Boynton converted both of his free throws on the other end to push Florida's lead to 66-63.
Lacey got a fairly clean look on the last-gasp 3-point attempt, but it was short. The Tide shot 56.5 percent from the field (13 of 23) in the second half and outrebounded Florida 32-27 for the game.
"I thought we got a good look," Alabama coach Anthony Grant said. "I thought it had a chance to go in, but unfortunately, it didn't go in our favor."
Now Alabama will have to wait before finding out if it will advance to the NCAA tournament for the first time since 2006.
"Obviously, we feel good about what we have been able to accomplish over the course of the season," Grant said. "We just have to wait and see what happens."