The Heat wasted a huge comeback and let what would have been their second win in as many nights to open the season slip away.
Philadelphia stormed to a 23-2 lead only to see the Heat climb within two by halftime. Miami scored 80 points during the second and third quarters and owned a nine-point cushion heading into the final period.
Carter-Williams boosted the Philadelphia lead to two with a free throw that came with 28 seconds left, Turner added two more from the line with 18 remaining and Carter-Williams finished off the scoring with another two foul shots.
Miami managed just two points over the final four minutes.
Hawes added 24 points and Carter-Williams had 22 for the 76ers, who won just 34 times last season.
LeBron James led Miami with 25 points and 13 assists. James has 21 assists in his first two games, the first of which resulted in a win over Chicago to begin the campaign on Tuesday.