Brad Marchand also scored for the Bruins and Tim Thomas turned in 28 saves.
The victory was the third in a row for Boston.
Glencross scored on a power play at 17:27 of the third period to cut the Boston lead to 2-1, but Lucic knocked in an empty-netter to push the Bruins' lead back out to two goals.
Lucic opened the scoring just 59 seconds into the first period. Marchand made it 2-0 early in the third period with his 25th goal of the season.
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