Cunningham knocked down 9-of-12 at the free-throw line for SMU (24-9), which will play LSU in the second round. Ben Moore added 11 points, Nick Russell scored 10 and Nic Moore dished out eight assists.
For UCI (23-12), the regular-season champions of the Big West Conference, Luke Nelson had 13 points, Alex Young netted 10, Mamadou Ndiaye contributed 12 rebounds and seven blocks and Will Davis II hauled in 11 boards.
Although UCI outshot SMU from the field in the first half, 52.2 percent to 29.4 percent, it only took a one-point lead into intermission, 30-29. The Mustangs kept the game close by attempting 11 more field goals than the Anteaters and by shooting 7-of-11 at the foul line.
The tables were turned in the second stanza, with SMU shooting 40 percent from the field to UCI's 24.1 percent. The Mustangs continued their busy night at the foul line with a 16-of-23 showing over the final 20 minutes to hold off the Anteaters down the stretch.
UCI was plagued by a game-high 20 turnovers, which SMU turned into 19 points.