In the sixth meeting between Buffalo and Boston, Buffalo won 4–1 and thus won the series 4–2.
Rasmus Dahlin was highly involved in the win when he provided two assists, the first for the 1-0 goal when he played the puck to Alex Tuch.
The second came in the final stages of the match when Dahlin poked the puck out of a tangle to Josh Norris, who scored the final goal, 4–1, from the blue line into an open net.
"It means a lot. We will enjoy what we have accomplished, but there is much more to do. It has been a very long period, especially for me and Rasmus Dahlin who have been here." Buffalo star Tage Thompson told the NHL's website.
The club will face either Montreal or Tampa Bay in the quarterfinals. Both will play a seventh and decisive game on Monday night local time in Sweden.
Vegas also advanced to the quarterfinals overnight after a 5-1 victory over Utah. They will face Anaheim in the quarterfinals.
Round of 16:
Boston–Buffalo 1–4 (Buffalo advances to quarterfinals)
Montreal–Tampa Bay 0–1 in overtime (3–3 in games)
Utah–Vegas 1–5 (Vegas advances to quarterfinals)
