Simmons went out and backed Brown's talk with a pair of steals in the second half, including a game-clinching play down the stretch for the short-handed 76ers.
Joel Embiid had 27 points and 17 rebounds, James Ennis III scored 18 of his 20 points in the second half, and Philadelphia overcame a sluggish start and beat the Knicks 101-95.
"The league better pay attention to him defensively," Brown said of Simmons. "How can he not be discussed amongst the league's better defensive players? He guards five men, point guards, twos and threes. He's kind of a Swizz army knife in that regard."
Tobias Harris scored 19, and Simmons chipped in 16 points for the 76ers, who have won two straight and six of seven.
Julius Randle had 22 points and 10 rebounds, and Marcus Morris Sr. scored 20 points for the Knicks, who have lost a season-high five straight.
The Knicks, who have lost their two meetings this season against the 76ers, went 19 for 33 from the free-throw line.
"At the end of the day, you've got a guy like Joel Embiid and Ben Simmons out there, that's why they make the big bucks," New York coach David Fizdale said. "Those guys are closers. You just can't miss 14 free throws against a team like that."
The 76ers were playing without starters Al Horford (rest) and Josh Richardson (right hamstring injury) and it showed in the first half as their offense struggled. Philadelphia shot 13 for 38 from the field, including 2 for 18 behind the 3-point line.
But the Sixers rallied from a 51-39 halftime deficit, cutting the lead to 56-52 with 8:03 to play in the third quarter when Simmons intercepted Julius Randle's inbound pass off a time out and raced down the court for a dunk.
Philadelphia then outscored the Knicks 16-11 over the final seven minutes of the third quarter for a 70-68 lead entering the final quarter. The Knicks offense sputtered, going 0 for 9 with two turnovers down the stretch in the third.
Philadelphia went on a 9-3 run, capped by former Knick Trey Burke's basket that made it 79-73.
Harris increased the 76ers' lead 94-89 with 1:19 left in regulation, forcing a Knicks timeout.
Simmons, who entered play second behind former teammate Jimmy Butler with 2.25 steals per game, picked off an inbound pass from Frank Ntilikina and dunked to extend the lead 96-89 and hold off the Knicks.
Finding their offensive rhythm, Simmons said, would allow their offense to be on par with their defensive effort and avoid future starts like the one they encountered at Madison Square Garden against one of the league's worst teams.
"We got to know what we are good at, what we are great at, and what's working us," he said. "With this team, moving the ball, posting up, slashing, cutting and finding guys on the perimeter is what works."
The Knicks jumped out to a 23-9 lead on consecutive baskets from Barrett in the opening period. A 3-pointer from reserve Damyean Dotson made it 31-18 to close out the first.
New York led by as many as 16 points in the second after Philadelphia coach Brett Brown picked up a technical foul after question a foul call on Simmons.
Marcus Morris Sr. hit the technical free throw and Randle was perfect on his two free throws, extending an 8-0 run to make it 51-35.
76ers: C/F Horford was held out due to rest. ... G Richardson did not play because of tightness in his right hamstring.
Knicks: RJ Barrett had 18 points.
NEXT MAN UP:
Missing Richardson's 16.1 points and Horford's 14.4 points meant Brown had to reach into his bench to make up the difference and backup forward Ennis III certainly did not disappoint.
Ennis III went 3 for 4 from the 3-point line and was perfect on his nine free throws over 22 minutes after totaling just 24 minutes in his last two games.
His play was key late in the third quarter as the 76ers rallied. He contributed eight points during a 9-2 run to close out the period.
"I mean in this whole locker room he has a respect level with the way that he plays and how hard he plays and tonight it was coming to fruition in a high-volume way," Harris said. "But we don't come out of here with this win today without him, his effort."
76ers: Host the Indiana Pacers on Saturday night.
Knicks: Host the Boston Celtics on Sunday.
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Simmons, Embiid lead 76ers' comeback win vs. Knicks
Joel Embiid racks up a game-high 27 points and 17 rebounds while Ben Simmons adds 15 points and eight assists as the 76ers beat the Knicks 101-95.