Texas A&M (6-5, 3-4 Big 12 South) upset No. 2 Oklahoma last week but freshman quarterback Reggie McNeal suffered an apparent leg injury in the second quarter against the Tigers and did not return.
Long entered and had a decent day, but was picked off by defensive back Michael Harden in the second extra session.
That gave Smith, who rushed for 94 yards on 26 carries, an opportunity to win it with his short touchdown run. The Tigers also got 126 yards rushing from Zack Abron and finished with 259 yards on the ground.
The teams traded 40-yard field goals in the first overtime.
Abron scored on a nine-yard run and added an eight-yard touchdown reception in the second quarter as Missouri (5-6, 2-5) built a 17-3 halftime lead. The Aggies got a one-yard touchdown run by Joe Weber and tied it on Long's one-yard plunge to open the fourth.
Smith hit tight end Justin Gage, also a forward on the basketball team, for a 24-17 advantage with 8:40 left in the fourth quarter. But Long engineered a nine-play, 67-yard drive that Weber capped with another one-yard plunge with 15 seconds to go in regulation.
Long completed 22 of 35 passes for 270 yards, but the Aggies were held to a season-low 36 yards on the ground, their worst total since managing just two yards in a loss at Nebraska in 1999.
The Aggies finished 3-4 at home, their worst mark at Kyle Field since 1983.