Carrera finished with 18 points, while LaShay Page scored a game-high 22 for USC, which overcame 25 turnovers.
Missouri State (2-3) had a pair of three-point leads in the final 33 seconds of regulation but missed two critical charity shots down the stretch to open the door for USC.
Up 55-53 with 33.2 to go, Christian Kirk was intentionally fouled on a wide-open dive to the basket. He missed the front end, but converted the second to push the MSU advantage to three. Dorrian Williams was fouled on the ensuing inbound play after the Bears retained possession, but he missed the front end of the one-and-one, and South Carolina called a timeout to set up a play for Page who scored with 23.8 to go.
The Gamecocks then fouled Marcus Marshall, who had a team-high 17 points for MSU, and the freshman knocked down both free throws with 12.2 ticks left to push the Missouri State edge to 58-55. On the final sequence of regulation, the Bears' pressure defense had South Carolina in trouble as the Bears pushed USC point guard Eric Smith out near the timeline in the final seconds. Forty feet from the basket, Smith wheeled an off-balance pass to Carrera just right of the circle, and the freshman found nothing but the bottom of the net as time expired.
In overtime, Marcus Marshall was once again the step-up player for Missouri State as he knocked down an authoritative pull-up jumper just 22 seconds into the extra period. But the Bears would go the next four minutes without a field goal. During that span, MSU missed four field goal attempts, two free throw attempts and had two turnovers.
Meanwhile, the exhausted Gamecocks rallied behind the Bears' mishaps and got a floater from Brenton Williams to fall at the 1:43 mark of overtime as the shot clock expired to gain a 64-60 advantage. MSU would get no closer, as the Southeastern Conference foes made 10-of-12 free throws from there.
Williams sliced a 3-pointer through with 31.3 ticks left for the Springfield club, while Anthony Downing scored a pair of lightly-contested buckets late to account for the final seven-point margin.
Downing and Kirk each had 16 points for Missouri State, which finished 23-for-59 (.390) from the field and 5-of-19 (.263) from long range. More critically was the team's lack of free throw execution as the Bears missed out on 12 charity points, going just 16-for-28 (.571) at the line.
Missouri State was out-rebounded 33-29, but had a 22-17 rebounding edge after halftime, including seven by Keith Pickens in the second stanza. Pickens posted a game-high eight boards in all. The Bears had just 13 turnovers on the night and tallied a season-high 10 steals.
South Carolina also got double figures from Brian Richardson who scored 14 with four 3-pointers. The Gamecocks were 22-for-39 (.564) from the field and 8-of-18 from bonus range. USC was 22-for-28 (.786) at the foul line, including 14-of-17 after the half.
In the first half, Missouri State's swarming defense helped the Bears overcome a 16-7 rebounding deficit to lead 33-28 at the break. After the Bears jumped ahead 11-3 in the first three-and-a-half minutes, the MSU offense went cold, and the Gamecocks reeled off the game's next 13 points to take a 16-11 advantage.
A steal and layup by Downing with 8:32 left in the opening stanza broke an eight-minute stretch without a field goal for the Bears and made it a 19-16 game at the time. Downing would pull the Bears within two 36 seconds later with a solitary free throw, before a tough bucket in traffic by Kirk tied the game with 7:22 to go.
Later, Williams tied the game again with a floater in traffic, but momentum briefly went back to USC as it got a free throw by Jackson and an offensive rebound off his second miss that Mindaugas Kacinas converted into two points. The Bears rallied again for the final eight points of the period with a 3-pointer by Bruce Marshall, a put-back by Nathan Scheer and back-to-back steals by Downing that netted a layup and a free throw to put the maroon-clad squad ahead by five at the intermission.
Missouri State now awaits the loser of the second semifinal game between UALR and SMU. Tipoff will be at 6 p.m., Sunday for third place in the event.