Devin Hester picked up a blocked field goal try and returned it 78 yards for a score. Parrish brought a punt back 73 yards for a touchdown.
Hester added an interception for the 14th-ranked Hurricanes, who finished the season at 9-3.
Miami's Brock Berlin completed 13 of 23 passes for 171 yards and a touchdown. It was the sixth straight win for Miami over Florida.
Florida, which will be operating next season with a new coach, fell to 7-5. The Gators had finished the regular season with three straight wins.