Sims led by two with 18 seconds left in regulation, but missed an open layup that would have ended the game. Woodruff hit a last second shot to send the game to overtime.
The Tigers trailed by as many as nine points in OT, but fought back. With 20 seconds left, down by five points, Victor Ruth passed to Brett Smith, who nailed a 3-pointer.
Sims forced a five-second count on the inbound pass with its full court press. The Tigers got the ball with 10 seconds left and Garrett hit the winning three from the left wing.
“It could not have happened to a better player,” said coach Mitchell Moss. “Earlier he missed a big shot, but he had the belief in himself to take the shot and nailed it. It was the best game he has played all year.
“We would not have been in the situation if not for our team defense and Brett making his shot. It was an exciting game - a fight the entire game."
Garrett led the Tigers with 15 points and Devontae Glenn added 12.
Smith scored six points, while Ruth had four. Keiston Smith and Kadarius Means each scored two.
Sims improves to 6-4 on the season.
WOODRUFF - Sims' girls' basketball team defeated Woodruff 28-16 on Tuesday.
Kristin Giles led the scoring with 11 points, Logan Wade had eight points, Christa Green had four, Kelsey Turner had three and Lauren Harrison had two.
“It was a great win for us,” said coach Kelly Jenkins. “We played great defense and we got after every loose ball. I was proud of the hustle and intensity that they played with. They really wanted to win it.”
Both Sims teams travel to Fairforest on Thursday.