Former Senators goalie Alex Auld stopped 11 shots in his first outing with the Canadiens. Mayer took over 9:38 into the second.
Kostitsyn gave Montreal a 2-1 lead 10:50 into the second when he jumped into the slot to intercept Ottawa veteran Chris Phillips' cross-ice pass before firing a low shot past Leclaire.
Darche put the Canadiens up by 3-1 with a power-play goal at 15:50, taking a feed from David Desharnais to finish off a nice passing play begun by defensemen Brendon Nash and Mathieu Carle.
Keller scored late in the second to draw the Senators to 3-2. Boyd restored Montreal's two-goal lead in the third.
The Northeast Division rivals will meet again Saturday night in Ottawa.