Coyle scored, and Jeremy Swayman made 33 saves for Boston (27-16-4), which played its third game without forwards Patrice Bergeron (head) and Brad Marchand (suspended).
"Both goalies were very good tonight," Bruins coach Bruce Cassidy said. "That's why it ended up 1-1 probably, a lot of good stops."
Chytil tied it 1-1 at 6:45 of the third period. He took advantage of Swayman losing control of the puck after making the save on his shot from the right circle. The Rangers forward got the puck, pulled it around Swayman's left pad and tucked it into the net.
"I saw it in and then it trickled out," Swayman said. "Obviously, I want that save back."
Shesterkin kept it tied at 8:42, when he made a glove save against Taylor Hall on a breakaway.
Coyle gave the Bruins a 1-0 lead at 3:39 of the first period, scoring on a rebound of Smith's shot.
Barclay Goodrow attempted a drop pass from the neutral zone across the Rangers blue line, but Coyle intercepted it and pased to Smith in transition. Shesterkin saved Smith's shot, but Coyle was able to knock the puck over the goalie's glove.
"We wanted to jump on them early and get the lead right away," Coyle said. "They had their pushes and all that, but 'Sways' played great."