It was the second straight game in which Buffalo held a late one-goal lead before scoring into an empty net, and the third in a row in which they protected a one-goal advantage in the final frame.
Mired near the bottom of the Eastern Conference for most of the season, the defending Presidents' Trophy-winning Sabres are aware of the importance of holding on.
"We have to be able to win those tight ones," Pominville said. "That's usually a sign of a good team. It's not every night you'll be able to score five or six goals."
After allowing Kane to score on Chicago's first shot, Miller was solid the rest of the way in his fifth straight start and 10th consecutive appearance. He made several big stops, including denying Kane's point-blank shot in the second period to preserve Buffalo's one-goal lead.
Miller also made a sparkling kick save on Tuomo Ruutu from in close with 6 minutes left in regulation, and kicked out Brent Seabrook's slap shot from the top of the right circle that seemed destined to go in minutes later.
"He made great saves to keep us in the game," Pominville said. "He's been playing well, and that's what we expect."
The slumping Blackhawks, meanwhile, have lost five of six overall, and four straight on the road.
"It was a game where the neutral zone was clogged pretty good," Chicago coach Denis Savard said. "They got one power-play goal and we didn't."
The game was Kane's first in his hometown. The No. 1 overall pick in this year's draft grew up about six miles from the Sabres' downtown arena, and had about 500 family and friends in attendance at the game.
"It was a tough game," Kane said. "There was a little bit of a distraction. I was probably the only one who could really get up for this game."
Kane received a warm ovation when his name was announced after he was called for a hooking penalty in the first period.
"The guy in the penalty box even said to me, 'You can't go wrong tonight,'" Kane said.
Kane opened the scoring at 2:35 of the first with his first goal in 14 games. From behind the goal line, Patrick Sharp fed Kane, who was just coming into the slot. Kane one-timed the puck past Miller along the ice for his eighth goal.
Vanek tied it with his 10th nearly 3 minutes into the second period on the power play. Standing in the slot, Vanek let go a quick wrist shot after accepting a pass from Roy, who was behind the goal line.
Stafford made it 2-1 midway through the second with his seventh. Stafford picked up a loose puck in the right circle, whirled around and whistled a wrist shot that eluded Khabibulin.
Pominville capped the scoring with an empty-net goal with 47 seconds remaining.
"We're taking more pride in playing defensively and blocking shots," Vanek said. "I think it's paying off."
Kane was honored before the game, with his father and grandfather dropping the ceremonial first puck. ... Because of Kane, the Blackhawks opened their morning skate to the public, and about 1,000 people showed up. ... This was the first matchup between the teams in Buffalo since a 1-1 tie in December 2002. ... Buffalo is 2-4 against the Western Conference. ... It was Chicago's only road contest during its current stretch of playing six of seven at home.
Copyright by STATS LLC and The Associated Press
Arena: First Niagara Center Location: Buffalo, New York
Referees: Tim Peel, Dean Warren Linesmen: Brian Murphy, David Brisebois
Attendance: 18,690 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Patrick Kane (8)
Assists: Patrick Sharp, Jonathan Toews
Thomas Vanek (10)
(Power Play) Assists: Derek Roy, Maxim Afinogenov
Drew Stafford (7)
Assists: Thomas Vanek, Derek Roy
Jason Pominville (8)
(Empty Net) Assists: Tim Connolly, Toni Lydman