The Heat celebrated their title ring presentation on Tuesday night with victory over the Chicago Bulls but were unable to follow that up, going down 114-110 to the 76ers at Wells Fargo Center.
Carter-Williams hit two important free throws late on as he finished with 22 points and 12 assists. The 11th overall pick in this year's draft even threatened a quadruple-double as he added nine steals and seven rebounds.
Evan Turner scored 26 points and Spencer Hawes 24 while for Miami, there were double-doubles for LeBron James (25 points, 13 assists) and Chris Bosh (22 points, 10 rebounds).
The Oklahoma City Thunder - who had last season's best record in the Western Conference - edged out the Utah Jazz 101-98.
All-Star forward Kevin Durant rammed in 42 points, including a late pair of free throws to ensure victory.
The other teams in Miami's South-east Division have made a winless start, with the Orlando Magic beaten for the second night running as the Minnesota Timberwolves won 120-115 after overtime. Kevin Love led the way with 31 points and 17 rebounds.
The Washington Wizards, Atlanta Hawks and Charlotte Bobcats lost to the Detroit Pistons, Dallas Mavericks and Houston Rockets respectively.
Detroit's win still leaves them behind Indiana in the Central Division after the Pacers became the season's first two-win team.
Paul George scored 32 points as the Pacers won 95-90 in New Orleans, in the hosts' first game since rebranding as the Pelicans.
Number one overall draft pick Anthony Davis had 20 points and 12 rebounds for the Pelicans, with Eric Gordon (25) and Jrue Holiday (24) also scoring highly.
The Cleveland Cavaliers also made a winning start in the Central Division, beating the Brooklyn Nets 98-94.
Dallas and Houston joined South-west rivals the San Antonio Spurs in winning their opening games. The Spurs were 101-94 victors over the Memphis Grizzlies, with six players scoring double figures.
Philadelphia's Eastern Division rivals the Toronto Raptors and New York Knicks enjoyed opening wins over the Boston Celtics and Milwaukee Bucks respectively.
Pacific Division trio the Golden State Warriors, Phoenix Suns and Sacramento Kings were all victorious, the former downing divisional rivals the Los Angeles Lakers 125-94 with a career-best 38 points from Klay Thompson.
Goran Dragic's 26 points led the Suns, under new coach Jeff Hornacek, by the Portland Trail Blazers 104-91 while Sacramento beat the Denver Nuggets 90-88 with DeMarcus Cousins contributing 30 points and 14 rebounds.