Williams knocked the ball away from a diving Isaiah Thomas on the final play of the game before Smart grabbed the loose ball under the basket and threw up a buzzer-beating shot to give the Boston Celtics a 117-116 overtime win over the Toronto Raptors.
Four seconds earlier, Williams had hit a three-pointer to give the Raptors a short-lived, one-point lead.
"I thought I did enough," Williams said of the final play. "I figure it's game. I thought I got the stop.
"It was just a bad bounce. It bounced right to Smart where he can just grab it and put it in. It was tough."
The final play, which was reviewed and the call upheld, thwarted a comeback by the Raptors, who trailed by 11 going into the final quarter and were down by six with 2:18 to go in the fourth. And, they did it while two of their starters — Kyle Lowry and Amir Johnson — sat out with injuries.
"That was a playoff atmosphere-type game, guys competed," said Raptors coach Dwane Casey. "We executed down the stretch, which is something we've been harping on and our guys did it.
"Undermanned or whatever you want to call it, the guys that stepped on the court competed tonight."
Toronto's DeMar DeRozan had 38 points to lead all scorers while Williams added 27 off the bench.
Tyler Hansbrough, who started in place of Johnson, scored 18 points and added eight rebounds before fouling out with 1:06 to go in overtime. Johnson sprained his ankle in Friday's loss in Brooklyn.
Thomas had 25 points for the Celtics while Tyler Zeller added 20 points and nine rebounds. Canadian Kelly Olynyk had 16 points off the bench for Boston (35-42).
Despite Saturday night's heart-breaker, DeRozan said the Raptors (45-32) will be able to learn from their mistakes as they get ready for the playoffs.
"That's the positive of it," he said. "To be able to look at the mistakes that we've made in late-game situations, two minutes, execution on both ends.
"Clean that up and understand that we've got to get better at that if we want to close out games."
The Raptors outscored the Celtics 10-4 over the final 2:18 to send the game to overtime.
DeRozan had Toronto's final eight points of the fourth quarter, including a five-foot jumper in the lane to tie the game at 104 with six seconds left to go. Thomas missed a three-pointer at the buzzer that would have won it for the Celtics.
Boston took a 81-70 lead into the fourth quarter after dominating the third.
DeRozan said being the Raptors' go-to guy down the stretch of games is "what you dream of when you are a kid.
"I know the ball is going to come to me in a lot of those situations," DeRozan said. "My whole thing is just be calm. Never feel rushed and take whatever they give me, if that's me getting a shot or creating an open shot for my teammates."
On the three-pointer with 4.0 seconds to go, DeRozan drove inside and then found Williams.
"You've been around so long that you know not to get too excited," Williams said of his late basket. "I've been around this game so long and I've had many situations like tonight.
"There's some that have gone my way and some that haven't. Unfortunately, tonight it went the other way."