Kovacevic pocketed two assists while adding three shots on net, three hits and a plus-3 rating in Monday's 5-2 win over the Predators.
Kovacevic produced an assist, two shots on goal and two blocked shots in Tuesday's 4-2 loss to the Hurricanes.
Kovacevic scored a goal on one shot and registered an assist in Friday's 3-1 victory over New Jersey.
Montreal traded Kovacevic to the Devils in exchange for a fourth-round draft pick Sunday.
Kovacevic picked up two assists while logging a plus-2 rating in 19:28 of ice time in Tuesday's 9-2 win over the Flyers.
Kovacevic (undisclosed) will serve as a healthy scratch against Nashville on Tuesday.
Kovacevic had an assist, two blocked shots and one hit in Saturday's 4-3 loss to New Jersey.
Kovacevic scored a goal on three shots and had two hits over 15:15 of ice time in Tuesday's 4-1 loss to Ottawa.
Kovacevic scored a goal on one shot and had one hit over 11:23 of ice time in Sunday's 4-3 loss to the Lightning.
Kovacevic was a healthy scratch Thursday against Carolina.