Chicago's Marian Hossa scored a power-play goal with 4:19 left in the third period to tie it at 2. Patrick Kane also scored for Chicago, which had won three in a row.
Crawford made 27 saves.
The 26-year-old Berra was recalled from Abbotsford of the AHL on Saturday after the Flames waived Joey MacDonald. The 6-foot-4 Swiss goaltender was acquired in the trade that sent defenseman Jay Bouwmeester to St. Louis last April.
Berra was sharp against the Blackhawks, making a handful of point-blank and flashy stops.
After a slow start this season offensively, Chicago had scored 24 times in its previous five games. But the Stanley Cup champions showed little of that explosive skill and tempo against Calgary.
The Blackhawks outshot the Flames 18-11 in the scoreless first. Berra coolly swept away Chicago's routine chances and turned in a couple of tough stops, including a quick glove save on Andrew Shaw with 5:00 left in the period. Calgary's best chance came with 1:28 left, but Dennis Wideman's shot capping a 3-on-2 break was smothered by Crawford.
Wild 4, Devils 0 • In St. Paul, Minn., Josh Harding stopped 19 shots for his second shutout of the season and Minnesota beat New Jersey. Mikael Granlund, Torrey Mitchell, Dany Heatley and Jason Pominville scored for the Wild, who have won five of six. Nino Niederreiter had three assists.
Stars 4, Senators 3 • In Ottawa, Jamie Benn scored the winner in a shootout in the Dallas' victory over Ottawa. Senators goalie Craig Anderson went down hard after being hit by Valeri Nichushkin during overtime. He was taken off the ice on a stretcher after he appeared to take a knee to the head.