The Sixers, who hold the sixth spot in the Eastern Conference playoff race, trailed by as many as 13 points in the third quarter before storming back in the final period, going on a 20-6 run during the last five minutes of regulation.
Simmons finished with 13 points, 12 assists and 10 rebounds.
Dario Saric had 21 points and 12 boards, JJ Redick added 18 points and Robert Covington chipped in 15 for Philadelphia, which was able to rebound from a tough loss Tuesday night to the Indiana Pacers, who currently own the fourth seed in the East.
Michael Beasley had 24 points and 13 rebounds, and Courtney Lee and Trey Burke each contributed 16 points for the Knicks, who have lost a season-high nine straight games and 17 of 18. The Knicks' last win came on Feb. 22 at Orlando.
Kyle O'Quinn finished with 15 points and 10 rebounds, and Enes Kanter added 14 points and 10 rebounds for a New York team that has lost its last eight games at home. The Knicks haven't earned a victory at Madison Square Garden since beating Brooklyn on Jan. 30.
New York led 104-98 on Emmanuel Mudiay's jumper with 5 ½ minutes remaining in the fourth quarter before the 76ers mounted their comeback.
Covington's 3-pointer with 3:23 left capped an 8-2 run to put the visitors up 106-104. But Lee answered back with a 16-foot jumper to tie it up on the next possession.
Embiid was then fouled and made one of his two free throws to give Philadelphia the lead for good, 107-106 with 2:45 to go before Redick followed it up with a 3-pointer from the corner in front of the Knicks bench.
An errant pass by Beasley on the ensuing possession led to a 3-pointer by Saric behind the right wing to put the game out of reach at 113-106 with just 1:58 left.
76ers: Embiid became the first Sixers player to notch 40 20-point performances in a season since Andre Iguodala (2007-08).
Knicks: Mudiay had 12 points.
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Simmons joined Oscar Robertson and Magic Johnson as the third rookie in NBA history to reach 1,000 points, 500 rebounds and 500 assists. The 21-year-old Australian joined the special club when he picked up his fifth assist of the night in the second quarter, setting up Covington's 3-point basket.
76ers: Host the Brooklyn Nets on Friday.
Knicks: Continue their four-game homestand Saturday when they welcome the Charlotte Hornets.