The Tigers will take on Oklahoma State in Sunday's championship game after the Cowboys survived a late rally by Butler.
LSU had a nine-point lead with 13 minutes to play, but Memphis closed the game on a 29-13 run.
Jackson put Memphis in front at 66-64 on a layup with 3:40 remaining and he added a jump shot 12 seconds later. LSU trailed the rest of the way.
Austin Nichols paced Memphis with 19 points, Jackson had 16 and Chris Crawford added 15. Memphis will take a 4-1 record into its meeting with unbeaten Oklahoma State.
LSU (4-2) was led by 19 points from Anthony Hickey.