Morris joined the LSU baseball team in 1993, just out of high school in Alexandria, Louisiana. He did not receive an athletic scholarship to play baseball, but made the team while on academic scholarship as a second baseman. He did not play at second base in his first season at LSU, because the Tigers already had All-American Todd Walker at the position. Morris did see action at other positions. Walker went pro after the 1994 season, and Morris would become the team's starting second baseman from 1995 to 1996. His best season at LSU came in 1995. He would hit .369 with 8 home runs, 50 RBI, and 18 stolen bases.
LSU was expecting big things from Morris in 1996, but a broken wrist kept him out of the lineup for 42 games that season. He did rejoin the team in time for the 1996 postseason, which would include the College World Series. However, the wrist injury still lingered. He could not hit for power, and was placed at the bottom of the lineup.
LSU reached the championship game of the College World Series in 1996, and was trailing Miami 8–7 in the game with two outs in the bottom of the ninth inning. Morris came up to the plate with one runner on base, and hit Miami relief pitcherRobbie Morrison's first pitch just inches over the right field fence. The walk-off home run won the game for the Tigers 9–8. It was his only home run of the season, and is the only walk-off championship-winning home run in College World Series history. In addition, it is the only 2-out, ninth inning, walk-off home run in a championship of any collegiate or professional level. The home run also won Morris the 1997 Showstopper of the Year ESPY Award.