With his team down by nine and only 6:04 to play in the fourth, Drury scored the first two of his 15 points in the frame to lead Kelly (2-8) back from the brink and on to a 68-64 win.
"Trey hit a few clutch threes and we had a few clutch free throws," Kelly's Gabe Felter said. "We just came together tonight in the second half."
Their fortunes in the fourth were a big turnaround for the Hawks after having been outscored in each of the previous two quarters.
Kelly had came out of the first quarter with a 17-14 lead, but were outscored by nine and three points in the second and third quarters respectively to fall behind 44-35 entering fourth.
It was almost two minutes into the final frame after the two teams had already put up four points each that momentum seemed to swing the Hawks way.
Starting with two free throws from Drury and capped by a Felter basket from inside the paint, Kelly opened a 9-4 run up in just under two minutes that brought Kelly back to within four at 52-48 with 4:41 to play.
A few minutes later, the Hawks were finally able to complete their comeback when Drury connected on a 3-point shot from the right corner to tie the game at 57 with 2:17 to play before hitting a jump shot a few seconds later to give Kelly the lead.
"Those are big shots for a kid like him to step up and just have confidence to shoot," Hawk's head coach Josh Eftink said. "The kid has a lot of faith in his shot and it's a good one."
Though Chaffee (7-5) quickly came back to tie on a basket by Andrew Terhune, Kelly was able to take the lead once and for all with 1:20 to play when Drury hit one last shot from behind the top of the arc to put his the Hawks up by three.
"We seen what the score was and we just put it on them," Drury said of Kelly's fourth quarter turnaround. "That's what we had to do."
While Chaffee was able to pull back to within one at with seven seconds left on a shot by Jason Cicardi, Kelly's Ian Householder was able to connect on both free throws when fouled on the Hawks' next possession.
Putting the game to rest, Kelly fouled Cicardi on the Red Devils next possession, forcing him to the line where he missed both attempts.
Coming away with the ball following the free throws, the Hawks made one of their final two shots from the line with 2 seconds left to seal the game.
"Even when they second quarter didn't quite go the way we wanted and we got down, the kids still knew that they had it in them to play the way they needed to," Eftink said. "Today a big difference is they didn't get in a big hurry. They ran through the offense and got some easy shots when they needed it.
"That's one of things when you hang around and hang around you build confidence with everything. You've got guys that are finally starting to show what they've been showing me all year in practice and games. It's starting to click a little bit."
Besides Drury, who had a game-high 19 points, Ian Householder was another key cog in the Hawks' comeback. Householder finished the night with 18 points, scoring 11 of those in the fourth, including going 6 of 7 from the line in the final frame while also hitting a 3-pointer.
As for Chaffee, the Red Devils finished the night with four scorers in double-digits with Jordan Yahn lead the way with 14. Terhune 13 left hime second on the team while Cicardi and Crowe had 12 apiece.
"Through three quarters we did all right, holding them to 35 points," Chaffee head coach Josh Govreau said. "Giving up 33 points in the fourth is not going to win you any ball games.
"I told them after the third quarter if you continue to let a team like that hang around they will just play with more confidence at the end and they proved that. Everything they were throwing up in fourth quarter was going in."
Earlier in the evening, Chaffee's junior varsity defeated Kelly's junior varsity 44-32. Layton Tenkhoff and Charlie Montgomery led the way for the Red Devils with 14 points each.
KELLY (68) -- Stosh Lovett 2, Trey Drury 19, Sawyer Elfrink 4, Michael Kuykendall 3, Ian Householder 18, Garrett Alsup 8, Jarret Nicoson 2, Gabe Felter 12. FG 14, FT 5-8, F 18. (3-pointers: Drury 2, Kuykendall 1. Fouled out: Alsup)
CHAFFEE (64) -- Alex Crowe 12, Blake Sencboy 1, Michael Rutherford 7, Jason Cicardi 12, Zach Dannenmueller 3, Jordan Yahn 14, Alex Davie 2, Andrew Terhune 13. FG 24, FT 13-22, F 17. (3-pointers: Crowe 2, Rutherford 1. Fouled out: none)