Kesler fired a high shot past Antti Raanta to help Vancouver end a two-game losing streak. Mike Santorelli was successful in the first round as the Canucks improved to 2-4 in shootouts.
Patrick Sharp had Chicago's only shootout score against Lack in the third round.
Lack, a rookie backup, said he got some advice from No. 1 goaltender Roberto Luongo and just tried to react.
"When you're in it, you don't really think about it," Lack said. "It's just like the AHL. You're just focused on what you're going to do next, and anticipate it."
The Canucks were playing their second game in two nights and third in four overall. But it also was a good time for Vancouver to turn to Lack after Luongo gave up soft goals at critical times in the previous two games, both losses.
Lack entered in the second period of Vancouver's 4-1 loss at Dallas on Thursday after Luongo allowed four goals on 19 shots.
"He stopped some world-class players there in Toews and Kane right off the bat, and that set us up for the win," Kesler said.
Vancouver's Daniel Sedin tied it at 2 with 9:12 left in the third period. Zack Kassian also scored for the Canucks, who trailed 2-0 after Kane set up Kris Versteeg's score in the first and then scored his team-leading 21st goal in the second.
"We came in late last night, and usually the first 10, 15 minutes, you try to survive," Sedin said. "We did that; I thought we knew if we kept it close we'd have a chance."
Kane has six goals and 14 assists during an 11-game point streak, helping him climb into second in the NHL scoring race behind Pittsburgh's Sidney Crosby. He also has at least one point in 23 of his past 24 games.
Raanta, also a rookie backup, had 22 stops in his sixth straight start since No. 1 goalie Corey Crawford suffered a lower-body injury Dec. 8.
The Canucks killed all four Chicago power plays to improve to 30 for their past 31 on the penalty kill. Vancouver, which entered with the NHL's best penalty-killing percentage, ended Chicago's string of power-play goals in 10 straight games.
"I thought our power play might have let us down a little bit tonight," Kane said. "We didn't really create any momentum off of it, and they probably got momentum off them killing them off, so it's something we'll try to improve on."
The Canucks had trouble clearing the puck early in the first, and the Blackhawks took advantage. Versteeg opened the scoring at 7:49 on a deflection of Kane's shot from just inside the right point.
Leveraging two power plays, the Canucks dominated early in the second and launched the first nine shots of the period. Raanta stopped them all during the flurry, including Sedin's deflection from the slot.
Kane then capitalized on Chicago's first chance in the period. Lack stopped Johnny Oduya's drive from the left wing, but Kane jumped on the rebound.
Kassian cut it to 2-1 at 8:19 when he snapped off a shot from the right circle. It went between the legs of Chicago defenseman Brent Seabrook and past a screened Raanta.
Santorelli had a chance to end the game in overtime but he hit the side of the net, just wide of the right post, after he broke in alone.
The Blackhawks recalled veteran G Jason LaBarbera from Rockford of the AHL. With Crawford still out, Chicago acquired LaBarbera from Edmonton last week. ... Vancouver was without injured D Alex Edler (knee, eighth game) and D Ryan Stanton (ankle, second game). ... Lack posted a shutout in his previous start, on Dec. 9 versus Carolina.
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CHICAGO, IL - DECEMBER 20: Jason LaBarbera #30 of the Chicago Blackhawks particiaptes in warm-ups beofre a game...