Both teams missed chances to win it in regulation before the Grizzlies pulled away over the final 2 minutes of overtime to hand the Warriors their first home loss of the season.
Conley had missed 10 of his 18 shots before sinking a wide-open jumper from beyond the arc to give Memphis an 82-79 lead. After Prince followed with a 21-foot jumper, Bogut scored on an alley-oop from Andre Iguodala to cut the gap to 84-81.
Prince made another long jumper and Gasol added two free throws for the Grizzlies.
Golden State, which had won four straight since losing to Memphis by 18 on Nov. 9, fell short in a bid to match its best start since 1991-92.
Curry was held out after sustaining a mild concussion from hitting his head on the floor diving for a loose ball during Golden State's win at Utah on Monday. The Warriors' second-leading scorer, Curry sat on the bench but received a rousing ovation from the crowd when a video tribute of his record-setting 3-point season from a year ago played on the scoreboard.
That forced coach Mark Jackson to shuffle his lineup. Iguodala ran the point in Curry's absence, finishing with 14 assists, while Harrison Barnes made his second start of the season.
It worked early for the Warriors.
Barnes had 10 points in the first quarter to help Golden State build a 26-16 lead. The Warriors also got a lift when Iguodala split a double-team by Gasol and Conley near the top of the key and dunked.
A pair of jumpers from Thompson pushed Golden State's lead to 32-20 in the second. Memphis, which shot 35 percent in the first half, couldn't get closer than seven and trailed by 10 at halftime.
The Grizzlies trailed by seven early in the third when Randolph and Conley scored four points apiece as part of a 10-0 run that helped give Memphis a slim lead heading into the fourth.
Randolph, who had 23 points and 11 rebounds in the first meeting between the teams, struggled with his shot most of the night and finished 9 of 22 from the floor.
NOTES: Jackson was unsure whether Curry would play Friday against the Lakers. "We're fortunate, because looking at the video it could have been a lot worse," Jackson said. "We'll continue to keep a close eye on him." ... Golden State backup center Ognjen Kuzmic broke his right pinkie in the first half.