Sam Young finished with 19 points and a career-high eight rebounds as Memphis gave coach Lionel Hollins his 100th victory. Rudy Gay had 14 points and 10 rebounds, and Darrell Arthur added 12 points. Tony Allen scored 10.
Corey Maggette led the Bucks with 22 points, including 20 in the third quarter to help Milwaukee erase a first-half deficit. John Salmons had 18 points and six assists, while Brandon Jennings finished with 16 points.
Conley's 3-pointer with the shot clock running down capped five unanswered points for Memphis, breaking a 77-all tie with 2:58 left.
The Bucks got no closer than three down the stretch as Memphis hit seven of its eight free throws in the final 19.6 seconds, sending the Bucks to their sixth loss in seven games.
It was the Grizzlies' second consecutive win, and it stopped a four-game road winning streak for the Bucks in the series.
Memphis stayed a game behind Portland for eighth place in the Western Conference playoff race. The Trail Blazers defeated Toronto 102-96.
Memphis opened the fourth with an 8-2 rally, erasing a 68-63 Milwaukee lead at the end of the third.
The Grizzlies led 45-40 after a sloppy first half. The Bucks shot 35 percent and committed nine turnovers, while Memphis shot 44.4 percent with a handful of miscues.
But the game had little flow at that point, and there were a lot of lineup combinations, leading to sporadic offense. Milwaukee's starting front line of Maggette, Ersan Ilyasova and Andrew Bogut managed only Bogut's two points, missing seven of their eight shots in the half.
Bogut ended the game with five points on 2-of-9 shooting.
Young hit all five of his shots in the first half for 13 points to lead Memphis, while Salmons led the Bucks with 10 points.
Memphis led the entire first half, stretching the lead to as many as nine points.
The Bucks immediately erased the Memphis lead in the third quarter with five 3-pointers, including four from long range by Maggette, to comprise a 16-2 run for a 56-47 lead. Milwaukee extended the lead to 11 in the quarter.
Maggette had 20 in the period as the Bucks outscored Memphis 28-18. That gave Milwaukee its five-point advantage entering the fourth.
NOTES: Bucks G-F Chris Douglas-Roberts, who played college ball at Memphis, sat out with an illness. ... Maggette entered the game playing well on the road, averaging 15.3 points per game versus 10.5 at home. ... Memphis G Jason Williams saw his first action for the Grizzlies after signing earlier this week. He played 4 minutes and did not score.