Ottawa played its first home game of the season after contesting its opening six contests on the road. It was the Senators' second straight win following three consecutive losses.
New Jersey fell to 0-4-3 and has gone winless through the first seven games of a season for the first time in the history of the club.
Karlsson and Bobby Ryan both scored in the first period and the Senators made it 3-0 on a tally from Zack Smith with 1:19 to go in the second.
Craig Anderson made 40 saves to collect the victory. Brodeur allowed four goals on 22 shots.