Tim Connolly, Toni Lydman and Tim Kennedy also scored for Buffalo. The Sabres won their third straight to finish 3-1-1 on a five-game trip.
Derek Roy and Thomas Vanek each had two assists.
Sergei Samsonov, Brandon Sutter and Eric Staal scored for the Hurricanes, eight points behind Boston in the chase for the final playoff spot in the Eastern Conference.
The Hurricanes beat division leaders Pittsburgh and Washington in their previous two games but struggled against the Northeast-leading Sabres, who extinguished most of the drama with a four-goal second period.
After Connolly scored on the power play in the first, Hecht scored consecutive goals early in the second to build the Sabres' lead.
The first came when Hecht charged up the right side and quickly changed from backhand to forehand and smacked the puck through goalie Justin Peters' legs.
Hecht made it 3-0 when Peters overplayed his rush along the left boards, allowing Hecht to wrap the puck around the far side of the net.
Manny Legace replaced Peters at the 8:45 mark of the second after Peters couldn't stop Lydman's wrist shot on a 2-on-1.
The Hurricanes scored their first goal 12 seconds after Lydman's goal, with Samsonov deflecting Brett Carson's wrist shot past Miller.
Buffalo built its lead back to four almost immediately. Kennedy accelerated to the net past Carolina defenseman Brian Pothier, received a pass from Vanek and beat Legace with a nice backhand deke.
The Hurricanes added two goals in the third — Sutter on a shot from the side boards; Staal on a slap shot on the power play.
The Sabres are nine points ahead of Montreal and Ottawa in the Northeast and return home for consecutive games against their nearest rivals.
The teams split the four-game season series. … Hecht has five points in four games against Carolina. … Hurricanes defenseman Jamie McBain has five points in his first four NHL games.
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