Smith recorded his third shutout of the season for the Coyotes, who pushed their winning streak to a season-high five games.
"My teammates did a great job in front of me tonight," Smith said.
Chicago is trending in the opposite direction. The Blackhawks suffered their eighth consecutive loss and 10th straight on the road. They fell to 0-5-1 on a season-long nine-game road swing.
"We need something to give in and make us feel good about ourselves," said Chicago captain Jonathan Toews.
Ray Emery stopped 24 shots in defeat.
Radim Vrbata opened the scoring 3:14 into the contest with his team-leading 26th goal of the season.
Vrbata gathered a loose puck in the Chicago zone after a failed clearing attempt and accepted Ray Whitney's return feed. The crafty winger skated behind the enemy cage and sent a wraparound that Blackhawks defenseman Sami Lepisto directed into his own net.
Brule also picked up the primary assist on Kyle Chipchura's tally at the 12:59 mark of the middle stanza.
Smith posted 16 saves in the third period to preserve his 14th career shutout.
The Coyotes inducted former alternate captain Jeremy Roenick into the team's Ring of Honor in a pre-game ceremony on Saturday night...Whitney has two goals and 10 assists during an eight-game point streak...Phoenix earned its fourth consecutive win at home...The Coyotes won the season series, 3-1.