The Australian registered 20 points, 11 rebounds and seven assists for the Joel Embiid-less hosts.
But it was his willingness to play a power game that proved the difference, with Simmons at one point breaking down the court alone, dropping a shoulder into Chicago's Lauri Markkanen and nailing a poster dunk over the seven-foot Finn.
Simmons was not alone, with Furkan Korkmaz stepping up to net a career-best 24 points including six three-pointers.
The veteran, who has played for five teams during his 17-year career, needed just eight points to join the elite club and recorded his eighth and ninth with five minutes left in the first quarter.
Anthony's milestone was a rare highlight for the Trail Blazers as they lost 120-112 to the Mavericks, with Luka Doncic scoring 35 points.
In other games, the Indiana Pacers closed out a 116-114 triumph over the Minnesota Timberwolves, the Toronto Raptors won 140-111 against the Washington Wizards and the Oklahoma City Thunder rallied late but still fell to a 115-108 loss to the Miami Heat.
The Cleveland Cavaliers came agonisingly close but the Memphis Grizzlies finished 113-109 winners, securing their seventh straight victory, while the Atlanta Hawks won in San Antonio for the first time since 1997 when Kevin Huerter nailed a three-pointer with six seconds left to register a 121-120 victory over the Spurs.