Brian Elliott had 32 saves for the Flyers (6-6-1), who lost their second straight game and fourth in their past five (1-3-1).
Philadelphia went 0-for-3 on the power play, including one in the third period when they had five shots on goal.
The Flyers played the final two periods without defenseman Radko Gudas, who sustained an upper-body injury in the first period. They already were without two of their top six defensemen because of injury, Shayne Gostisbehere (upper body) and Andrew MacDonald (lower body).
Anisimov's power-play goal at 8:58 of the second period ended a 0-for-18 drought with the man-advantage that spanned five games. He won a face-off after Flyers defenseman Brandon Manning was penalized for holding, and got to the net to score on the rebound of Cody Franson's one-timer from the left circle.
"It's more relief," Anisimov said. "Something dropped from our shoulders when we scored that goal."
Blackhawks coach Joel Quenneville said the goal was the result of the power-play unit playing the right way.
"That turned out to be a big goal for us," he said. "Those couple earlier power plays had decent looks, but as far as doing the right thing on that one, get it to the net, get traffic at the net, get the rebound, get rewarded. We need a power-play goal. I think it helped the confidence as we went along."
Moments later, Flyers defenseman Robert Hagg fanned on a shot at the Blackhawks blue line, and Toews pounced on the loose puck for a breakaway. He made a forehand/backhand deke and slid the puck between Elliott's pads at 9:18. It was his fourth goal of the season and first in eight games.
Philadelphia outshot Chicago 15-12 in the third period, but the only goal was by DeBrincat, who scored into an empty net at 18:11.
"I thought we got traffic to the net, we had good opportunities all the way through," Flyers coach Dave Hakstol said. "Third period we had seven or eight really good scoring chances, we just didn't have anything to show for it."
