Shaking off a 23-foot miss at the second-half buzzer, Napier scored nine of his 24 points in overtime to lead seventh-seeded UConn (27-8) to an 89-81 win over 10th-seeded Saint Joseph's (24-10) in the second round of the NCAA tournament on Thursday night.
DeAndre Daniels scored 18 while freshman center Amida Brimah forced overtime by completing a three-point play in the final minute.
It was a big victory for Ollie, who took over two years ago after Calhoun was forced to step down because of health issues. After the Huskies won three national titles in 26 seasons under Calhoun, Ollie became the first UConn coach to lead the program to a tournament berth since Dom Perno in 1979.
And it came a year after Connecticut was barred from postseason play because of academic sanctions.
Langston Galloway scored 25 points for Saint Joseph's (24-10). The Hawks wore down because of a lack of depth, and then lost their top forward Halil Kanacevic, who fouled out early into overtime.
The Huskies advance to play Saturday, when they'll face the winner of an East Region game between No. 2 seed Villanova and No. 15 Milwaukee.
With the game tied at 70 entering overtime, Daniels opened the scoring by completed a three-point play with 3:47 left during a 5-minute period the Huskies never trailed. Napier then scored seven straight points - five of them coming from the line - to put the Huskies up 82-74 with 55 seconds remaining.
The game turned in the final minute of regulation and after Hawks guard Chris Wilson hit two free throws to put Saint Joe's up 70-67 with 49.2 seconds left.
Napier missed on a drive at the other end, but Brimah got the rebound to the left of the basket, and was fouled while putting it back. He tied the game by hitting the free throw.
Taking over with 39 seconds left, the Hawks never got a shot off on what became their final possession of regulation.
Galloway twice lost the ball on the dribble, but got it back both times, before launching a desperation shot that hit off the side of the backboard as the shot clock expired.
With 2.7 seconds left, the Huskies made two nifty passes to get the ball to Napier on the fly, who pulled up just before the 3-point line and had his shot hit off the rim.
Losing Kanacevic was a costly blow for the Hawks, who have little depth beyond their starting five.
Kanacevic finished with 12 points and seven rebounds. Freshman DeAndre Bembry scored 16 points for a Hawks team that won the Atlantic 10 tournament title last weekend.
After hitting 13 of their first 20 baskets, the Hawks offense cooled. Saint Joe's went 10 of 22 in the second half, and finished the game going 27 of 54.
The Huskies were coming off a 71-61 loss to Louisville in the American Athletic Conference title game on Saturday. They've now won 10 of their past three, with two of those losses coming against Louisville.
The opening nine minutes of the game featured eight lead changes before the Hawks eventually broke the game open by building a 37-27 lead with 3:09 left, when DeAndre Bembry hit two free throws. The Hawks hit 13 of their first 20 attempts and were up 40-32 before UConn's Ryan Boatright hit a 3-point basket with 8 seconds left.