Nick Pringle led the SEC champions with 19 points, one of four Alabama players in double figures. The Crimson Tide hit 15 three-pointers en route to a second-round matchup with eighth seed Maryland.
"March, Survive and advance, I think that's what we did", said head coach Nate Oats. "It was a good offensive game. Our defense has to get a lot better by Saturday. It was nice to come out and make some shots."
Trevian Tennyson led Texas A&M-Corpus Christi (24-11) with 20 points. The Islanders, who won their first-ever NCAA Tournament game in the First Four on Tuesday night, shot just 34.7 percent from the floor.
Crimson Tide roll past Islanders
Alabama, playing as a number one seed in the NCAA Tournament for the first time in school history, established themselves straight from the opening tip, racing out to a 9-0 lead, seven of those points coming from Noah Clowney.
Texas A&M-Corpus Christi closed the gap thanks to good bench work from Owen Dease, his three cutting the deficit to 19-15 with 11:49 left in the first half.
The Crimson Tide connected on five three-pointers midway through the opening 20 minutes and they went on a 7-0 run to build a 31-17 advantage.
Mark Sears was the latest Crimson Tide player to heat up on the offensive end, three straight from long-distance stretching the lead to 37-23 with 7:20 left.
A 54-34 lead marked the fifth time the SEC champions scored 50 or more points in the first half of a game. They connected on 10 of 17 from three and shot 53 percent from the field.
The Islanders opened the second half on a 10-3 run keyed by a pair of triples from Tennyson, forcing Alabama to call a timeout as the lead shrunk to 57-44.
Again, the Crimson Tide put together a 7-0 run to build the lead back up to 20 and a layup by Isaac Mushila kept the Southland champions down 20 at 70-50.
Dease and Tennyson brought Texas A&M-Corpus Christi to within 81-65, but the Islanders could get no closer, Ross Williams hitting a three as time expired for the final margin.