Maxey scored 27 points, while James contributed 20 points to help Philadelphia overcome a late Knicks challenge and secure its second victory over the reigning NBA champions this season.
Elsewhere, Giannis Antetokounmpo recorded a triple-double to lead the Miami Heat to a 145-125 win over the Indiana Pacers, while Kyrie Irving and Cooper Flagg powered the Dallas Mavericks to victory over the previously unbeaten Houston Rockets.
Maxey and James deliver as 76ers overcome Knicks
Philadelphia looked in control for much of the contest against New York, building a 14-point advantage in the third quarter.
However, the Knicks fought back and briefly moved ahead when Jalen Brunson converted a step-back three-pointer to make it 90-89 with 1:32 remaining.
James responded with a crucial basket to put the Sixers back in front. He then added a late tip-in following a Maxey miss, helping Philadelphia establish a five-point cushion and close out the game.
Maxey finished with 27 points to lead the Sixers, while James recorded 20 points, nine rebounds and eight assists.
Brunson led the Knicks with 24 points, while Karl-Anthony Towns contributed 22 points and 12 rebounds.
The victory gave Philadelphia its second win over New York this season, following its opening-night success at Madison Square Garden.
Giannis leads Miami past Indiana with triple-double
In Miami, Antetokounmpo delivered an outstanding performance, recording 31 points, 17 rebounds and 10 assists as the Heat defeated the Pacers 145-125.
Bam Adebayo added 27 points, while Klay Thompson scored 25 points, including seven three-pointers, to help Miami secure its second consecutive victory.
Indiana started strongly, taking a 42-36 lead after the opening quarter. However, the Heat responded with a 22-7 run late in the first half before extending their advantage with another strong spell after the interval.
Quenton Jackson led the Pacers with 24 points, while Andrew Nembhard added 22. Indiana were without injured guard Tyrese Haliburton and had only 11 players available.
The result gave Miami a winning start to its NBA Cup campaign, while Indiana suffered its third consecutive defeat.
Mavericks end Rockets' unbeaten start
The Dallas Mavericks produced a second-half comeback to defeat Houston 116-111, handing the Rockets their first loss of the 2026-27 season.
Kyrie Irving led Dallas with 35 points, while rookie Cooper Flagg added 33 as the Mavericks overturned an eight-point deficit entering the fourth quarter.
Irving's three-pointer with just over seven minutes remaining put Dallas ahead, and the Mavericks held on despite Houston's attempts to recover.
The result ended Houston's unbeaten start and gave Dallas an important victory in its NBA Cup group campaign.
Other results from Friday's NBA Cup action
Several other teams also began their group-stage campaigns with victories.
• Boston Celtics 125-111 Chicago Bulls: Payton Pritchard scored 30 points off the bench, while Jayson Tatum added 26.
• Detroit Pistons 110-94 Brooklyn Nets: Cade Cunningham scored 20 points as Detroit handed Brooklyn its fifth consecutive defeat.
• Orlando Magic 121-114 Toronto Raptors: Desmond Bane scored 28 points and Franz Wagner added 26, despite Scottie Barnes recording 41 points for Toronto.
• Minnesota Timberwolves 127-101 LA Clippers: LaMelo Ball scored 24 points and Jaden McDaniels contributed 23 in Minnesota's victory.
• Washington Wizards 95-79 Charlotte Hornets: Anthony Davis led Washington with 25 points, while Trae Young added 21.
• Golden State Warriors 112-95 Los Angeles Lakers: Stephen Curry scored 31 points, including eight three-pointers, while Luka Dončić finished with 37 for the Lakers.
• Phoenix Suns 127-120 Denver Nuggets: Jamal Murray scored 39 points and Christian Braun added 31 to lead Denver to victory.
NBA Cup group stage begins
Friday's games marked the opening night of the fourth edition of the Emirates NBA Cup, the league's in-season competition.
The group-stage matches will take place throughout November, with teams competing for places in the knockout rounds. The tournament provides another opportunity for teams to compete for silverware while their group-stage results also count towards the regular-season standings.
Philadelphia and Miami made winning starts, while Dallas also recorded an important result against Houston as the competition got under way.