Sam Young finished with 19 points and a career-high eight rebounds as Memphis gave coach Lionel Hollins his 100th victory. Memphis stayed a game behind Portland for eighth place in the Western Conference playoff race.
"The win shows how deep this team is," Conley said. "We have a lot of guys who can step up to the occasion and take a different role."
Rudy Gay had 14 points and 10 rebounds, Darrell Arthur added 12 points and Tony Allen 10 as Memphis played without leading scorer and rebounder Zach Randolph, who suffered a sprained right ankle near the end of the Grizzlies' 105-101 overtime victory at Oklahoma City on Tuesday night.
Memphis had to overcome Maggette scoring 20 of his 22 points in the third quarter to capture the victory. Maggette was 6 of 9 in the period, including 4 of 6 outside the arc, putting Milwaukee up by as much as 11.
"When you hit the first one, then you hit the second one, then the third one is kind like a heat check, and you go from there," Maggette said. "The team was putting me in position to make shots."
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.
"We scratched and clawed," Hollins said. "We thought it was going to be easy. We wanted it to be easy. During one of the timeouts, I told them winning is not easy. Even when we have everybody, it's not easy."
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. Milwaukee struggled from the field with the game on the line, shooting 25 percent in the fourth quarter on 5 of 20 from the field, including missing 11 of their first 12 shots in the fourth.
"We couldn't get stops down the stretch," Salmons said. "Offensively, we couldn't execute like we wanted to. That's kind of been our Achilles' heel the whole year, being consistent on the offensive end."
It was the Grizzlies' second consecutive win, and it stopped a four-game road winning streak for the Bucks in the series.
Memphis opened the fourth with an 8-2 rally, erasing a 68-63 Milwaukee lead at the end of the third.
"I think it was more defense than anything," said Memphis center Marc Gasol, who had nine points and eight rebounds. "When you get a couple of stops and players are talking to each other, that leads to defensive stops. Defense is always key."
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.
"They struggled to score, and we were struggling to score ourselves," Hollins said.
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.
The Bucks immediately erased 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's 20 in the period helped the Bucks outscored Memphis 28-18. That gave Milwaukee its five-point advantage entering the fourth.
It was a lead the Bucks couldn't maintain.
"We got hot there a bit in the third," Bucks coach Scott Skiles said. "Corey knocked down some 3s. He bailed us out of our offensive troubles temporarily, but we couldn't get enough guys to participate."
Bucks G-F Chris Douglas-Roberts, who played college ball at Memphis, sat out with an illness. ... Maggette entered playing well on the road, averaging 15.3 points per game while averaging 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. Memphis' last home win over the Bucks was April 7, 2006.