Rookie Miller netted what proved to the winner 15:58 into the second, after Carl Soderberg and Torey Krug had scored earlier in the period to erase Peter Holland's opener.
Jarome Iginla and Patrice Bergeron also tallied for Boston, while Jay McClement scored Toronto's second - his first of the season - at the start of the third.
Philipp Grubauer made 30 saves for his first NHL win as the Washington Capitals beat the New York Rangers 4-1.
Jason Chimera, Steve Oleksy, Mikhail Grabovski and Nate Schmidt scored for the Capitals.
Mike Santorelli had two goals and an assist as the Vancouver Canucks overcame the Colorado Avalanche 3-1.
The Chicago Blackhawks beat the Florida Panthers 6-2 and the Minnesota Wild were 3-1 winners over the San Jose Sharks.