Tim Quarterman provided the Tigers (19-12) with 12 points in 12 minutes off the bench, while Johnny O'Bryant tallied 11 points, six rebounds and four assists.
Jarell Martin had 10 points, Jordan Mickey posted nine points and 11 boards and Anthony Hickey dealt out eight assists. LSU will play No. 2 Kentucky in the quarterfinals on Friday.
For Alabama (13-19), Shannon Hale and Trevor Releford scored 11 points each. Levi Randolph contributed 10 points in the losing effort.
LSU knocked down 6-of-13 attempts from beyond the arc in the opening period en route to a 35-24 halftime lead. The Crimson Tide missed both of their free- throw attempts and connected on only 37 percent of their shots from the floor in the first half.
Alabama continued to struggle offensively as it was held to just 34.8 percent shooting from the field after the break. The Tigers made good on 52 percent of their field goal tries in the second stanza to keep Alabama at bay.
LSU outscored the Crimson Tide, 26-20, in the paint and enjoyed a 38-31 edge in total rebounds.