CHICAGO - As a boy growing up in Buffalo, it was always Patrick Kane's dream to play for his beloved Sabres.

Now one of the NHL's top players, Kane no longer holds on to that dream.

"Not really anymore," the Blackhawks winger said. "It was a dream up until you get drafted and you start your career here. I'm pretty content with where I am in my career, especially being here in Chicago."

These days, it's pretty much everyone's nightmare to play for the Sabres, who hit town with a league-worst one point earned in their first five games and on a downward spiral after missing the playoffs the last two seasons.

Kane and the Hawks made sure the Sabres left Chicago still spinning after they handed them a 2-1 defeat Saturday night at the United Center. Kane scored the game-winner on the power play and Ben Smith also found the back of the net to provide the offense for goaltender Corey Crawford, who withstood a Sabres onslaught in the third to secure the victory.

"It was good to win a tight one like that - it's never an easy game," said Crawford, who made 28 saves - 12 in the third period. "They kind of hung around there. Their goalie kept them in it (with) some big stops. It definitely wasn't easy. They gave us a test at the end."

Ryan Miller was stellar in goal for the Sabres but the only offensive support the veteran received was Drew Stafford's score in the final 10 minutes. Miller stopped 38 shots as the Sabres fell to 0-5-1. The Sabres' total of six goals in their first six games equals a franchise low set during the 1970-71 season.

The Hawks (3-1-1) controlled play throughout the first period and finally solved Miller as Smith notched his first goal of the season when he redirected a long shot from Brent Seabrook.

The tide began to change in the final two periods as the Sabres often had control of the puck, but a penalty gave the Hawks a man advantage and Kane extended the lead as the clock wound down in the second with a rocket past Miller following a nifty cross-ice pass from Patrick Sharp.

"It's a thrill every time you score a goal and to do it against a team that you grew up watching and ... pretty much your childhood was, 'When do the Sabres play and do I have time to watch or go to the game?'" Kane said. "It's something that probably doesn't sink in until your career ends, but it's pretty special playing against them."

Stafford cut the deficit in half midway through the third to make matters tense for the crowd of 21,261.

"We outshot them and had a lot of pressure to get that third goal and put them away (but) instead of scoring the third one we let one in," Hawks defenseman Niklas Hjalmarsson said. "But we got the two points and we have to learn from it and be better next game."