The Spurs took a six-point lead into the fourth quarter, but could not hold on while playing without injured stars Tony Parker and Manu Ginobili. Both could be out until the middle of December.
Milwaukee's comeback allowed the Bucks to halt a three-game losing streak. San Antonio, which had been trying to win back-to-back games for the first time this season, has only two victories.
After the Bucks had taken a four-point lead, San Antonio's Michael Finley made a three-pointer with 12.3 seconds to go.
Sessions was fouled by Tim Duncan and made one of two free throws with 11 seconds to go, giving Milwaukee an 80-78 lead.
Duncan then missed a leaner in the lane with four seconds left, after which Jefferson made two foul shots for the final margin of victory.
Jefferson scored 19 points and pulled down nine rebounds. Duncan led the Spurs with 24 and Finley had 19.