The Champions League hopefuls recorded a narrow away win courtesy of a single Oscar Cardozo strike in the closing stages of the game
The Lisbon giants came close to opening the scoring early on when Ezequiel Garay beat his marker in the air after a corner-kick, but his powerful header went inches wide.
They had another good chance in the closing stages of the first half when Pablo Aimar had a sight of goal, but the Maritimo goalkeeper proved to be too much of an obstacle.
Maritimo were dealt a huge blow only minutes after the interval when Olberdam received his second yellow card of the match, and Benfica eventually took advantage of their extra man on the pitch when Cardozo tapped home from close range to make it 1-0.
Benfica sit joint first in the league table with Porto. Both sides have collected 30 points from 12 games.