Asplund scored Buffalo's second goal just under five minutes into the second period.
Buffalo had taken the lead already in the first and in powerplay Asplund sent in the puck after assists from Rasmus Dahlin and Victor Olofsson.
But the Swedish trio was not finished there.
The match went to overtime with the score 3-3, then it became a blue-yellow show again.
Dahlin sent a pass to Asplund who in turn gave it to Olofsson.
The shot was covered for a return that Asplund certainly sent in to match-winning 4-3 and his second goal of the match.
It was Buffalo's fifth victory in seven games.