McAvoy scored a power-play goal on three shots and had one blocked shot, two hits and four penalty minutes in Thursday's 6-4 win over the Canadiens.
It took McAvoy just four seconds to score after Joel Armia went to the penalty box for tripping. It was the second goal in as many games for McAvoy, who also had an assist in Tuesday's season-opening loss to the Panthers. He recorded 13 of his 47 points last season while Boston was a skater up.