"I just closed my eyes and hoped he's not going to score," Bryzgalov said.
Kane hit Bryzgalov in the chest with his shot, and the Coyotes made the most of their second chance. Radim Vrbata, who scored his fourth goal in three games during regulation, added the only goal of the shootout as Phoenix won its fourth in a row by beating the slumping Blackhawks 3-2 on Saturday night.
The Coyotes, who were 2-9 after regulation before winning in overtime at Dallas Wednesday, suddenly look like the team that led the NHL with 16 wins after regulation last season. The four-game winning streak ties their second-longest of the season and moved them a point behind the Stars for the Pacific Division lead.
Phoenix has beaten the defending Stanley Cup champions in five of the last six meetings.
"They really played well from the start and even in overtime we needed Bryzie to stop Kane," said Vrbata, who had scored just four times in 20 games before catching fire. "Once he made that stop, we had a lot of confidence going the shootout."
Confidence continues to elude the Blackhawks, who are 2-4-2 in their last eight games and ended a 2-2-2 road trip with shootout losses on back-to-back nights. They blew a 3-0 lead in Dallas on Friday and rallied from a two-goal deficit in Phoenix, only to suffer the same result. Jonathan Toews, Kane and Marian Hossa came up empty in the shootout, with Kane and Hossa missing the net completely.
"(Coming back) shows a lot of character, but we have a lot of character in this room," said Chicago goalie Corey Crawford, who made 23 saves and two more in the shootout. "What we need is points."
The Blackhawks remain 11th in the Western Conference, six points behind fifth-place Phoenix and three behind eighth-place Minnesota.
The game was played before a crowd of 17,125, Phoenix's second home sellout of the season -- though much like the home opener against Detroit, it was dominated by fans rooting for the visitors. The electric atmosphere was matched by a high-energy game on the ice, but not many goals.
The Blackhawks came out flying from the start, taking 10 of the game's first 13 shots. But Bryzgalov stopped Toews on a backhander and got a break when Patrick Sharp fanned on a half-empty net during one dominant shift.
Then with the Blackhawks still pressuring, the game turned. Ray Whitney caught the Chicago defense pinching and sent Vrbata off with a pass off the boards. Vrbata deked around Crawford before stuffing in his 15th goal at 15:06.
Looking for more production, Coyotes coach Dave Tippett juggled his lines to begin the second period, moving captain Shane Doan alongside Pyatt and Eric Belanger. The decision paid off immediately. Just 42 seconds in, Pyatt took a Doan feed, used Chicago defenseman Jordan Hendry as a screen and beat Crawford with a shot that clanged off both posts before going in. Pyatt's 14th goal extended his scoring streak to four games and gave Phoenix a two-goal bulge.
But while the Coyotes bottled up the Blackhawks in 5-on-5 play, two ill-advised Phoenix penalties gave them new life.
Chicago had just two shots in the first 12 minutes of the second period before Phoenix's Lauri Korpikoski took a holding the stick penalty in the offensive zone. Hossa fed Brouwer in the slot for a one-timer that caught the top corner of the net at 13:17 and the Hawks were back in the game.
The Coyotes again had control in the third when defenseman Adrian Aucoin tried to flip the puck out of the zone -- but it fluttered into the crowd for a delay of game penalty with 4:19 left in regulation. The Hawks needed just 17 seconds for Duncan Keith to use a Brouwer screen and blow a bomb from the point past Bryzgalov to tie the game.
Chicago outshot the Coyotes 5-1 in overtime, but Bryzgalov stopped them all - and at least four of them with his eyes open. He has allowed just four goals during the four-game winning streak.
"He's big in the net right now and he's giving our team confidence," said Tippett, who won his 350th NHL game Saturday. "That was a heck of a save (on Kane). That's one they call a game-saving save."
The injury-plagued Blackhawks recalled former Coyote Jeff Taffe from Rockford of the AHL to replace Ryan Johnson, who was placed on IR with an upper body injury. Fernando Pisani (upper body) also sat out, while Hossa returned after a bout with the flu. The Coyotes got defenseman Ed Jovanovski (upper body) back for the first time in five games.