Ed Davis added 14 points and nine rebounds for Memphis, which improved to 19-19 and returned to the .500 mark for the first time since Dec. 9 (10-10).
The Grizzlies also won for the ninth time in 13 games despite no points in 14 minutes from Marc Gasol. It was the second game in two days for the NBA's reigning Defensive Player of the Year after he missed 23 contests with a left MCL sprain. He had 12 points in 24 minutes Tuesday against Oklahoma City.
Brandon Knight scored 27 points on 10-for-17 shooting for Milwaukee, which lost its seventh consecutive game.
A layup by Conley gave Memphis a 78-67 lead with 3:47 remaining before Milwaukee answered with an 8-0 run. Two free throws from Knight trimmed the Grizzlies' lead to 78-75 with 1:44 left.
Memphis then missed its next four shots, including three on one possession to give Milwaukee a chance. But Sanders missed a game-tying 3-point attempt -- the first of his career -- from the top of the arc with 2 seconds left and the Grizzlies held on.
Memphis scored the first 12 points of the final quarter and forced Milwaukee to miss its first 10 shots to beat the Bucks for the sixth straight time.
A tip-in by Davis tied the score at 60 with 11:12 to go and then Johnson scored eight consecutive points. After a dunk and two layups, Johnson stole the ball from John Henson for another dunk to give his team a 68-60 lead. A follow dunk by Davis capped the run and put the Grizzlies up 70-60 with 6:32 to play.
A jump shot by Knight gave Milwaukee a 60-58 lead at the end of the third quarter, the Bucks' first advantage since 8-7.
Milwaukee struggled mightily in the beginning, missing 16 straight shots in a span of 10:05. The Bucks clanked their final 13 field goal attempts of the opening quarter, and their 10 first-period points equaled their lowest total of any quarter this season.
But Memphis' halftime lead was only 42-35 after Milwaukee scored the final seven points of the second quarter.
Notes: Memphis also won four games in a row Nov. 15-20. ... Milwaukee was held to just 10 points in the first quarter Saturday at Oklahoma City. ... Lee finished with nine points, one day after scoring a season-high 24 against the Thunder. Milwaukee's Ersan Ilyasova also had a season-high 29 points Monday at Toronto. Against Memphis, he managed only four points on 2-of-11 shooting. ... Milwaukee is 3-15 at home and 1-11 overall against the Western Conference.