Watters, Connecticut's high school player of the year last season, scored seven points during a 13-0 LSU run that put the Tigers (1-0) up 48-27 1:39 before halftime.
A 10-0 LSU run pushed the lead to 61-34 early in the second half, and the Tigers' lead hovered around 40 points over the game's final eight minutes.
Watters was 9-for-13 shooting, including 4 of 6 from 3-point range.
Duop Reath and Wayde Sims scored 11 points each for the Tigers.
LSU shot 61 percent from the field and made 11 of 18 3-point shots.
A.J. Mosby led Alcorn State (0-1) with 15 points, and Reginal Johnson added 12 for the Braves, who shot 39.8 percent for the game.
LSU made its first six shots to take a 17-4 lead less than five minutes into the game. But Alcorn State responded with a 9-1 run as Tyler Carter hit a 3-pointer to bring the Braves to within five.
The Tigers were 7-for-10 from beyond the arc in the first half.
Wade inherited a Tigers team that was 10-21, 2-16 in the SEC and suffered through a school-worst 15-game losing streak.
Fans in Baton Rouge anticipated LSU's new up-tempo style under Wade. More than 11,000 people packed the Pete Maravich Assembly Center, the largest crowd for an LSU home opener in 20 years.