Miami is now 46-4 at home during postseason play under coach Jim Morris.
The Regional Championship is the 25th in school history and it gives the Hurricanes their first 50-win season since 2004.
Jackson was named Most Outstanding Player of the Regional as six Hurricanes were named to the all-tournament team. The sophomore shortstop hit .545 (6-of-11) with two home runs and four runs batted in regional play.
Ole Miss pulled within 3-2 on a two-run homer by Cody Overbeck, his 17th of the season. Raben's two-run blast to right-centerfield in the third gave Miami a 6-2 lead. It was his ninth of the season.
Raben, Weeks, and Jason Hagerty each drove in two runs for the Hurricanes, who have won seven straight games.
Nathan Baker (3-6) took the loss pitching 2 1/3 innings allowing six runs--five earned.
The Hurricanes are expected to host the NCAA Coral Gables Super Regional. The NCAA will make the official announcement Monday night at 11 p.m.