Nazem Kadri, Mikhail Grabovski and Frazer McLaren each provided a goal as the Leafs notched their first victory against Boston since a March 31, 2011, road victory.
Toronto won despite being outshot 33-13.
Anton Khudobin started in net but was pulled in third period after turning aside 8-of-11 shots.
Tuukka Rask made a pair of saves to close out the loss.
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