Miller wasn't heavily tested by sputtering Chicago, which lost its fourth straight. He lost a bid for his second shutout of the season when Denis Arkhipov scored a short-handed goal with 49.1 seconds left in the game. The Sabres improved to 7-2-1 in their last 10 with their second straight win. They have 65 points, tied with Anaheim for the league lead.
Chicago is 1-6-0 in its last seven games following a 9-3-3 stretch immediately after Denis Savard took over as coach on Nov. 27.
Buffalo centre Chris Drury was able to return to the game midway through the second period after hobbling off the ice early in the first.
Drury suffered what seemed like a potentially serious injury at 7:54 of the first when he was struck in the leg by a shot from teammate Jaroslav Spacek and then cross-checked by Chicago defenceman Duncan Keith.
Drury was standing in front of the Chicago net during a Buffalo power play and was knocked down legally by Keith. After Drury got back to his feet, Spacek's drive from the right point hit him.
Keith then cross-checked Drury after he was struck by the puck.
Drury, who has 22 goals and 19 assists in 41 games, was helped off the ice by two teammates and went directly to the Sabres' dressing room.
Hecht scored the only goal of the first period, at 4:47.
Nikolai Khabibulin, making his 16th straight start, stopped Jason Pominville's shot from the slot and followed with a pad save on Hecht's first rebound attempt from the left edge of the crease. Hecht, who was left unchecked, then jammed in a second rebound.
Afinogenov made it 2-0 at 2:56 of the third with his 20th goal. After skating down right wing, he slid a shot between Khabibulin's pads from a sharp angle.
Miller made one of his few tough saves - point-blank on Chicago's Craig MacDonald - with just over two minutes left.
With 49.1 seconds left and Khabibulin on the bench, Miller lost his shutout bid. Arkhibov's shot hit the post, then Miller's pads and deflected over the goal-line.
Notes: Blackhawks LW Martin Havlat sat out his third game with a pulled groin. D Jassen Cullimore missed his second game with a shoulder injury. . . . Chicago C Mikael Holmqvist was a healthy scratch. . . . The Blackhawks sent G Patrick Lalime, who hasn't played this season following surgery on a herniated disk, to Norfolk of the AHL for conditioning. . . . Buffalo D Henrik Tallinder missed his third game with a sprained ankle.