Poitras, a 19-year-old forward, gave Boston a 2-1 lead with his third goal of the preseason, scoring off a pass from Trent Frederic from behind the net.
Charlie Coyle scored, and Jeremy Swayman made 22 saves for the Bruins, who finished the preseason 2-2-2
Kaapo Kakko scored for the Rangers, who were 1-5-0 in the preseason. Igor Shesterkin made 12 saves.
Kakko scored from the slot at 10:14 of the first period to give New York a 1-0 lead.
Coyle tied it 1-1 at 11:13 of the second period.
A.J. Greer scored an empty-net goal with 22 seconds left in the third for the 3-1 final.
