Beno Udrih added 11 points and Tayshaun Prince contributed 10 for the Grizzlies, who played a fourth consecutive game without inside star Zach Randolph, who has a knee injury.
Dwyane Wade, whose 31-point performance sparked Miami over Cleveland and ex-teammate LeBron James two nights earlier, scored 25 points while reserve Danny Granger scored 18 points and Britain’s Luol Deng added 16.
The Heat fell to 14-17 and have not won back-to-back games in more than a month.
Memphis took a big lead but Miami trimmed the deficit to a single point several times in the fourth quarter only to fall short of overtaking the Grizzlies each time.
Conley’s floater gave Memphis a 93-86 lead with 2:54 remaining. Mario Chalmers’ three-point play and two Chris Andersen free throws pulled the Heat within 93-91 but Gasol added two free throws and later blocked a Chalmers shot in the closing seconds to seal Miami’s fate.
Heat forward Chris Bosh missed his eighth game in a row with a left calf strain.