"We had enough looks to tie it up but couldn't do it," Rangers coach Alain Vigneault said.
The Blackhawks took a 2-1 lead on Anisimov's goal with 1:09 remaining in the second period. It came after a diving stick save by Darling on Mats Zuccarello 34 seconds earlier.
"You can only worry about the next shot, but it's nice when you make a big save like at the end of the second and the guys go down and score a goal," Darling said. "It's nice to contribute to stuff like that."
Darling made 15 saves in the second period and 11 in the third. He stopped Marek Hrivik on a rebound and Jimmy Vesey at the left post with his left pad with 2:07 left.
"He's been unbelievable," van Riemsdyk said. "A couple highlight-reel saves there that just leave you saying, 'Wow.' He's been awesome. He's so steady. He's making all the saves. He's doing a great job handling pucks. He's been great, and we have a ton of confidence in him too."
Van Riemsdyk ended Raanta's shutout streak by scoring on a far-side shot from the right hash marks off a pass from Artemi Panarin.
"I think I overplayed it a little bit, slid a little bit too hard and their [defenseman] made a good play and just put it in the empty net backdoor," Raanta said.
Fast tied it when he batted the puck into the net from in front of the left post. Darling made 18 saves after the goal.