Hammonds, who scored all of his points in the opening half, had two critical three-pointers as Clemson closed the period with a 12-1 run.
Booker had 15 of his points in the second half, when the Tigers extended their lead to as many as 19.
Mississippi, the SEC's West champion, ended its first season under coach Andy Kennedy at 21-13.
The Rebels were trying to extend their first postseason appearance since 2002. But their high-scoring backcourt of Clarence Sanders and Bam Doyne managed only 18 points, 13 fewer than their combined averages. Todd Abernethy led Mississippi with 18 points.
It was Clemson's largest postseason margin of victory, surpassing the 77-57 victory over Georgia in the 1999 NIT.
Kentucky coach Tubby Smith, whose Wildcats fell to Kansas in the NCAA tournament Sunday, traveled from Chicago to Littlejohn to pull for son Brian and his Rebels teammates.
Syracuse 80, San Diego State 64 - Demetris Nichols had 20 points, Andy Rautins scored 15, and Syracuse beat San Diego State before a tournament-record crowd in Syracuse, N.Y.
An orange-clad crowd of 26,752, the largest in NIT history, gave the game a championship atmosphere, and Syracuse (24-10), seeded second in the South, didn't disappoint, hitting nine three-pointers and stifling the sixth-seeded Aztecs (22-11) with some staunch defense.
San Diego State was one of three teams to pull a first-round upset on the road, beating third-seeded Missouri State, 74-70.
Air Force 83, Georgia 52 - Jacob Burtschi scored 21 points, and Air Force, at home in Colorado, won its school-record 25th game, a blowout of Georgia.
The Falcons (25-8), whose NCAA bubble burst with four straight losses to end the season, surpassed last year's win total in surprisingly easy fashion against a more athletic Bulldogs (19-14) team that was bothered by both the altitude and Air Force's zone defense.
Air Force advanced to the semifinals tomorrow night against DePaul at Clune Arena, where the Falcons have won 56 of their last 58 games.
Burtschi added 10 rebounds and Dan Nwaelele scored 19 points for the Falcons, the top seed in the West.
DePaul 70, Kansas State 65 - Sammy Mejia and Wilson Chandler led DePaul with 18 points each, and the Blue Demons won in Manhattan, Kan.
The third-seeded Blue Demons (20-13) reached the 20-win mark for the third time in four seasons and won two straight postseason games for the first time since the 1990 NIT.
Kansas State (23-12), the West's No. 2 seed, has not advanced past the second round in the postseason since reaching the NIT semifinals in 1994.