Oklahoma State (7-0) again came out flat to start a second half, one day after the Cowboys saw a 23-point halftime lead dwindle to four with 3 minutes to play before beating Purdue 97-87.
With the Cowboys holding a 68-67 lead in the final minute, Smart missed three free throws, including the front end of a 1-and-1.
Butler's Khyle Marshall was fouled with 8.4 seconds remaining, but missed both free throws.
Le'Bryan Nash made it 69-67 by hitting 1 of 2 from the line before Butler's Elijah Brown had his last second 3-point shot blocked by Michael Cobbins.
Nash added 15 points for the Cowboys, who will face the winner of the other semifinal between No. 21 Memphis and LSU in Sunday night's championship game.
Butler (5-1) got 15 points from Brown. Kellen Dunham, who set a tourney record with 32 points in Thursday's 76-69 victory over Washington State, finished with nine, while Marshall, coming off a 30-point performance Thursday, had eight.
This was the first meeting between the teams since Butler beat Oklahoma State 49-26 on Feb. 12, 1934.
Alex Barlow keyed Butler's initial surge by connecting on a pair of 3-pointers to get the Bulldogs within 48-41 5 minutes into the second half.
Phil Fotre made two long-range jumpers and Smart had a couple driving baskets as Oklahoma State responded and grabbed a 66-57 lead with 6 1/2 minutes to play.
Dunham and the Bulldogs made a final run, pulling within 68-65 with 3 minutes remaining when the guard hit a 3 and then converted a three-point play. Smart had the ball stolen by Erik Fromm on Oklahoma State's next possesion and Marshall got a rebound basket at the other end to make it 68-67.
Nash had 10 points, helping Oklahoma take a 44-30 halftime advantage. Five different Cowboys' had at least six points during the opening 20 minutes. Smart had a slam and Markel Brown made a jumper to give the Cowboys their biggest lead of the first half, at 44-28, 1:48 before the break.
Smart had 30 points in Thursday's tournament opener.