Boston also nearly blew a 3-1 series edge in the opening round this year against Toronto, before rallying from a three-goal deficit in the third period and capturing Game 7 in overtime.
Hamilton, who recovered from 9-5 down to edge Michael Holt 10-9 in the final qualifying round of the world championship last week, compiled breaks of 92, 47, 68, 87 and 77.
In the remaining second-round matches to be completed, Julien Benneteau won 6-0 in the fifth set to edge past Colombia's Alejandro Falla, while Florent Serra needed four tight sets to eliminate Romania's Victor Hanescu.
There is history hanging over Boston, including a blown 3-0 lead to Philadelphia in a series loss in 2010 and a squandered 3-1 edge in this year's first round to Toronto before the Bruins rallied to win Game 7.