Texas-San Antonio, which had won its last seven games and 11 of the last 12, took a 26-24 lead with 6 minutes, 5 seconds left in the first half on a basket by Frank Hampton.
But Illinois broke free from a tie at 28 as Hamilton scored on an alley-oop dunk and a rebound follow and Nick Anderson hit a jumper to make it 34-28 with 2:34 left.
After taking a 38-31 lead at the half, the Illini then scored eight of the first 10 points in the second half for a 46-34 lead.
Jens Kujawa added 10 points for Illinois.
Eric Cooper and Hampton each scored 17 points for the Roadrunners, with Scott Smith adding 13.
Kentucky 99, Southern 84 - Senior Ed Davender poured in a career-high 30 points and Rex Chapman added 23 to lead sixth-ranked Kentucky over Southern.
Kentucky (26-5), leading only 64-60, reeled off 11 straight points midway through the second half to seize a 75-60 advantage, and run-and-gun Southern (24-7) finally ran out of steam.
Southern's full-court pressure permitted the Jaguars to trade baskets with highly favored Kentucky for the first 30 minutes.
Southern was paced by Kevin Florent with 25 points and Daryl Battles with 20.
Kentucky will face Maryland in tomorrow's second round.
Maryland 92, Cal-Santa Barbara 82 - Derrick Lewis scored 18 of his 25 points in the second half as Maryland used its inside strength to defeat California-Santa Barbara.
Maryland (18-12) used its size advantage to wipe out a 44-39 halftime deficit and earn its first NCAA tournament victory for Bob Wade. The second- year coach replaced Lefty Driesell in the turmoil following the death of Len Bias.
Maryland will play Kentucky, a 99-84 winner over Southern, in a second- round game tomorrow at Riverfront Coliseum.
California-Santa Barbara (22-7) got off to a torrid start in its first NCAA tournament appearance, hitting 69 percent from the floor in the first half. But the Gauchos couldn't keep up with Lewis when Maryland took its offense close to the hoop after the intermission.
Lewis scored 14 of Maryland's 21 points in a 10-minute stretch to help the Terrapins take command with a nine-point lead. UC-Santa Barbara got no closer than three points in the final 10 minutes.
The first half was a long-range shootout, and the Gauchos got the best of it.
Each team opened the game with three three-pointers. UC-Santa Barbara went on to hit 7 of 10 three-point shots in the first half.