Eric Belanger and Kyle Turris scored 35 seconds apart in the second period for the Coyotes, who came into the game having lost three straight and four of five.
Bryan Bickell scored the lone goal for the Blackhawks, who have lost four straight games in front of their home crowd. Marty Turco was tagged for both goals on 22 shots.
The Blackhawks took the initial lead in the game at the 9:22 mark of the first when Troy Brouwer threw a shot on net that Bickell redirected past LaBarbera for his third goal of the year.
At the 6:23 mark of the second, Phoenix tied the game as Wojtek Wolski stickhandled his way past a Blackhawks defender and from the low left side threw it across the goalmouth where Turris redirected it in.
Moments later, the puck got behind the Chicago pointman in the Phoenix end and Belanger caught up to it. He skated down the right wing on a 2-on-1 break and opted to shoot from the right circle where he blew it past Turco for a 2-1 lead.
LaBarbera stopped 12 shots in the middle frame then made 10 saves in the third to help Phoenix hang on for the win.
The Coyotes took three of four from Chicago last season…The Blackhawks play in Nashville on Saturday…Phoenix hosts Calgary on Friday…Chicago center Dave Bolland missed his sixth contest in a row because of a rib injury…There was just one power play in the game and it belonged to Chicago, which failed to score on the opportunity.