Johnny O'Bryant III had 15 points and nine rebounds, and Andre Stringer added 11 points as LSU (17-10, 8-7 Southeastern Conference) won its seventh straight at home and improved to 13-2 in the Pete Maravich Assembly Center.
The Aggies (16-12, 7-8), who beat LSU in the teams' previous meeting in College Station, Texas, came into the game shooting a league-worst 40.7 percent in SEC games and fared even worse than that at LSU, shooting 30.8 percent (16 for 52).
Part of the Aggies' problem stemmed from the defensive play of 6-foot-8 LSU freshman Jordan Mickey , who blocked five shots.
Jordan Green led the Aggies with 12 points and Kourtney Roberson added nine points and eight rebounds.
Martin, a 6-9 freshman, made a season-high four 3-pointers on five attempts and also grabbed seven rebounds.
Anthony Hickey had eight assists to equal his career high which he set in an overtime loss at Kentucky just last Saturday.
LSU turned a six-point halftime lead into a double-digit advantage early in the second half thanks in large part to Martin, who scored nine straight LSU points on a 3, a jumper, two free throws and a fast-break layup, the last giving LSU a 43-31 lead with 11:54 to go.
Martin's Tiger teammates got back into the act with Stringer's 3-pointer and Shavon Coleman's layup to make it 48-33.
Texas A&M, meanwhile, was plagued by poor shooting. During the first 11 minutes of the second half, the Aggies made only 2 of 16 shots (12.5 percent), providing little indication they would be able to rally back from a 15-point hole in the final 10 minutes.
They never got closer than 13 the rest of the way.
The first half featured drastic momentum swings.
Antwan Space scored five early points, including a layup that gave A&M a 15-7 lead nearly 7 minutes into the game.
The Aggies then went 10 minutes without a single point, missing nine shots and turning the ball over three times during that stint.
LSU cashed in with a 21-0 run during which Stinger scored five of his points, first hitting a 3 and later a layup that capped the spurt and gave LSU a 28-15 lead.
Texas A&M finally broke its scoring draught on Alex Caruso's layup, and Dylan Johns' dunk capped a 9-2 run to close out the half and pull A&M to 30-24.