Coming off a disappointing loss to Dallas, the Coyotes charged at the Blackhawks following a pregame ceremony honoring the 1980 U.S. Olympic hockey team.
Keith Yandle scored 69 seconds in and had an assist on Radim Vrbata's goal late in the second period. Smith made it stand up with some tough saves late in the third period, closing out his second shutout of the season after rocker Alice Cooper played a three-song set during intermission.
Antoine Vermette extended his career-high point streak to nine games on Yandle's goal in front of a raucous, sold-out crowd.
Chicago had impressive victories in sweeping the two Southern California teams this week, but struggled offensively without leading scorer Patrick Kane, who left to attend his grandfather's funeral.
The Blackhawks allowed two power-play goals after killing off 32 of 33 penalties the previous 10 games. They couldn't solve Smith and now head into the Olympic break off their first shutout since Game 3 of the Stanley Cup finals against Boston last June.
The Coyotes have been agonizingly inconsistent, playing well against good teams and struggling against teams further down the standings.
Phoenix beat rival Los Angeles 3-0 in one of its best games of the season and followed that with a loss to Buffalo, which has the league's worst record. The Coyotes bounced back to beat Pittsburgh, then lost on Tuesday to Dallas, a team they are jostling with for a playoff spot.
They got off to a fast start against the Blackhawks, which came to the desert with 84 points, second-most in the NHL.
Yandle triggered it.
He was fired up by the 1980 U.S. Olympic team's appearance, fist-bumping every player as they went by the bench. Yandle, left off the current U.S. Olympic team, used that energy to score a power-play goal 69 seconds into the game on a hard slap shot from near the blue line.
After one shot in the opening 14 minutes, the Blackhawks turned up the pressure late in the first period and early in the second.
Smith stood his ground during Chicago's flurries and had stellar sequence late in the second period, when he slid over to stop a redirected shot by Jonathan Toews, then stopped a point-blank shot by Patrick Sharp, who stood in disbelief for a few seconds before looking back at the Coyotes' goalie.
A few minutes later, Smith ended up on his backside in the net with his mask lying in front of him after being run over by Brandon Saad. Defenseman Michal Rozsival was called for an unsportsmanlike after the play to give Phoenix a 5-on-3 and Vrbata capitalized quickly, beating Corey Crawford with a wrister from the slot.
Cooper kept the vibe going during the second intermission with ''I'm 18,'' ''No More Mr. Nice Guy'' and ''School's Out,'' and Smith made the shutout stand with some tough stops, including a nifty glove save on Saad after Chicago pulled Crawford for an extra attacker.
NOTES: Ten members of the Miracle on Ice team were present for the pregame ceremony and current Olympians on the Coyotes and Blackhawks also were recognized. ... Coyotes C Martin Hanzal missed the game due to an illness. ... Chicago D Johnny Oduya missed his second straight game with a lower-body injury. ... Vermette has eight goals and four assists during his point streak.