Tuukka Rask allowed only a second-period goal and made 32 saves to win his season opener after leading Boston to the Stanley Cup Finals last spring.
Chris Kelly scored Boston's first goal of the season midway through the first period with a penalty shot after he was pulled down by Mark Barberio on a breakaway.
Valtteri Filppula tied it at the 10:32 mark of the second period, but Lucic scored on a wrist shot with 60 seconds to go in the middle stanza.
Patrice Bergeron added a shorthanded goal early in the third.
Anders Lindback took the loss, surrendering the three goals on 25 shots.