Conley knocked down a pair of huge 3-pointers during a 12-2 surge that snapped a 91-91 tie and vaulted the Grizzlies to their 12th consecutive home victory. The win also kept Memphis within one game of Phoenix for the eighth and final playoff seed in the Western Conference.
Both the Grizzlies and Suns have four games left in the regular season, with the teams to square off in Phoenix this coming Monday.
Eighteen of Conley's points came after halftime, while Zach Randolph delivered 25 points on 12-of-15 shooting and pulled down 11 rebounds and Marc Gasol posted a double-double of his own, finishing with 20 points and 14 boards.
LeBron James racked up 37 points in a potentially costly defeat for the defending NBA champion Heat, who fell a half-game behind Indiana for first place in the East heading into Friday's colossal showdown between the clubs in Miami.
Rashard Lewis added 17 points in the loss, the Heat's third in four games.