Vrbata scored the lone goal of the shootout and the Coyotes twice came back from two-goal deficits to beat the Blackhawks 5-4 on Saturday night for their eighth straight win.
"It was the same as the last game," Vrbata said. "We fell behind but we went out and had a really good third period. We never want to quit, and we came back and found two points."
"The first game off the road can be a trap game," said coach Dave Tippett, whose Coyotes were perfect on their just-completed four-game trip. "But our guys answered the bell."
Lee Stempniak scored twice, and Adrian Aucoin and Wolski also had a goal each for the Coyotes, who moved within one point of San Jose for the Pacific Division lead and two points of the Blackhawks for the Western Conference's best record.
"I wanted to come here and have a fresh start," said Stempniak, who came to Phoenix from Toronto for a draft pick. "I've scored goals before and I know I can do it. To be part of a team that's winning and be able to chip in is a lot of fun."
The Coyotes' winning streak is one short of the franchise record and matches the team's eight-game streak from Nov. 6-Dec. 2, 1999.
Andrew Ladd and Sharp scored 73 seconds apart early in the third period, Troy Brouwer and Kane also scored, and Marian Hossa had a pair of assists for the Blackhawks, who lost for the fourth time in five games. Two losses came after regulation.
Chicago is 29-1-3 when leading after two periods.
"It's embarrassing," Chicago defenseman Duncan Keith said. "There's really no other way to say it or talk about it."
The Blackhawks were playing without defenseman Brent Seabrook, who missed his second game because of an upper body injury sustained when he was leveled by Anaheim's James Wisniewski on Wednesday. Wisniewski was given an eight-game suspension by the NHL for the hit.
Ladd snapped a 2-2 tie with 17:27 remaining on a knuckling shot from the top of the right circle. Sharp made it 4-2 from between the circles.
Stempniak scored on a rebound with 13:07 to go for his ninth goal in eight games since he was acquired by the Coyotes at the trade deadline to cut the lead to 4-3.
Aucoin tied the game when he fired home a loose puck in the low slot, capping a play started when Taylor Pyatt blocked a shot near the Coyotes' blue line.
"We've got to play defense," Blackhawks coach Joel Quenneville said. "We know we're going to score goals. We know we've got the offense."
Brouwer scored from the doorstep at 11:52 of the first to open the scoring.
Kane was left alone in the right circle during a second-period power play, took a cross-ice pass from Hossa, and beat Bryzgalov for a power-play goal that made it 2-0 at 5:11.
Wolski made it 2-1 at 9:20, backhanding the puck toward the net as he was pestered by a pair of defenders. The puck bounced off Shane Doan's skate to the top of the crease where Wolski swooped in and beat Niemi with a wrist shot.
Stempniak tied it with a power-play goal 1:11 into the third. He stood at the top of the crease and redirected Aucoin's shot from the point past Niemi.
"We've got to be able to play better," Ladd said.
Phoenix C Matthew Lombardi missed a penalty shot with 3:45 left in overtime. Stempniak has three two-goal games since coming to Phoenix. He had 11 goals with the Maple Leafs. The game was played in front of a season-high crowd of 17,534, besting the attendance from opening night by two. Kane's goal was his first since March 2, a span of nine games.