The defending national champion Huskies fell one game short of winning four times in four days and earning a trip back to the NCAA tournament.
Markus Kennedy led SMU (27-6) with 15 points.
Rodney Purvis scored a career-high 29 points for Connecticut (20-14), which became the sixth team to miss the NCAA tournament after winning the title the previous year since the field expanded to 64 in 1985. Ryan Boatright, who had been averaging 17 points in the tournament, finished with seven points and fouled out with 45 seconds left. He was one for 12 from the field.
SMU led by 17 points early in the second half, then held on as Connecticut cut the lead to five with 3:22 left. The tournament title was the first for the Mustangs since the 1988 team won the Southwest Conference.
Treveon Graham had 20 points and 13 rebounds and was selected tournament's most valuable player. Doug Brooks made the play of the game with a steal in the final minute when the Rams needed to stop trading baskets with the Flyers.
Jordan Sibert made three free throws with 10.6 seconds left for second-seeded Dayton (25-8) to make it 67-65, but VCU (26-9) closed it out from the free-throw line.
Georgia State Coach Ron Hunter, whose son R.J. made the deciding free throws with 21.6 seconds left, injured his Achilles tendon in the immediate postgame celebration and had to be helped off the court after his team's 38-36 victory over Georgia Southern (22-9) in the Sun Belt Conference tournament final at New Orleans.
"I tore my Achilles on the right side years ago playing basketball," Hunter said. "This was the exact same feeling and I knew when I jumped up … but instead of stopping right there, I wanted to go celebrate with my team. More importantly I wanted to go celebrate with my son. You don't get many opportunities like that."
Georgia State (24-9) prevailed in the lowest-scoring Sun Belt final since the University of New Orleans defeated South Alabama 22-20 in 1978 and the Panthers played without injured leading scorer Ryan Harrow, a University of Kentucky transfer.