After a scoreless first period, Östlund recorded his first point by setting up teammate Bowen Byram to tie the game eleven minutes into the second period.
Boston's Viktor Andersson had missed a penalty just a minute earlier.
Before the game was over, Östlund scored the decisive goal with a wrist shot with 1:24 left in the third.
With the victory, Buffalo, playing in the playoffs for the first time in 15 years, took the lead in the series, 2–1.
Round of 16:
Buffalo–Boston 3–1 (Buffalo leads 2–1 in games)
Carolina–Ottawa 2–1 (Carolina leads 3–0)
Los Angeles–Colorado 2–4 (Colorado leads 3–0)
