Jennings outscored the Thunder 8-2 in the final 2:21 of the game, hitting the go-ahead reverse layup with 56.8 seconds left and then hitting two free throws to put the game away.
Russell Westbrook scored 20 points and Kevin Durant added 14 in a season-low 23 minutes as the Thunder gave their starters a lightened load with the playoffs looming. Oklahoma City will be the No. 4 seed in the Western Conference and open against the Denver Nuggets in the first round.
Redd, in possibly his final game with Milwaukee, hit a 3-pointer to spark a 9-0 flurry in the final 86 seconds and send the game into overtime.
Redd, a second-round pick, has spent all 11 years of his NBA career with the Bucks, becoming an All-Star in 2004 and an Olympic gold medalist with the U.S. team in 2008. He missed most of the past two seasons after serious injuries to his left knee and didn't play this season until late March.
But he was on the court at the end to get perhaps his last win with Milwaukee.
Despite giving Durant and the rest of the starters a rest — and letting reserve Nick Collison sit out — the Thunder seemed to be in control even until the final minutes of regulation.
Oklahoma City's reserves let an 11-point lead slip away late in the first half, but Westbrook and Durant powered Oklahoma City back in front with an 18-5 push in the third quarter.
Durant got it going with a fast-break layup and Westbrook added eight points, finishing with a steal that led to a right-handed, fast-break dunk to put Oklahoma City up 66-55 with 4 minutes left in the third quarter.
Thunder coach Scott Brooks kept his starters on the bench again for the whole fourth quarter, eventually using even the last player on the bench in the final few minutes.
The Bucks took advantage, with Redd's 3-pointer from the left wing starting the final rally. John Salmons hit three free throws with 23.1 seconds left to tie it at 96, and Nazr Mohammed missed a shot from the free throw line in the final moments of regulation that could've given Oklahoma City the win.
The Thunder then missed a chance to tie the NBA record with a ninth overtime win this season.
Oklahoma City got out to a 35-24 lead against the cold-shooting Bucks, only to let the lead slip away when Brooks opted to let his starters rest instead of putting them back in the game late in the second quarter.
Milwaukee finished the first half on a 15-1 run to go up 46-43 at halftime.
NOTES: Before the game, Oklahoma City hung a banner commemorating its Northwest Division title in the rafters — fittingly in the northwest corner of the arena. Banners of the franchise's accomplishments in Seattle are not on display, so it's the first banner on display. ... Referee Joe Crawford switched out the game ball for a backup late in the first quarter after both teams complained about it. Milwaukee made just five of 17 shots with the original ball. ... Thunder C Cole Aldrich was on the inactive list after being recalled from Tulsa of the NBA Development League prior to the game.