Benfica join Porto in exiting Portuguese Cup
Coach Jorge Jesus's decision to make several changes to his starting line-up seemed to be paying off when Argentine forward Javier Saviola put Benfica in front with a first-half penalty.
Midfielder Roberto Sousa then levelled for Maritimo, who are fourth in the league, with a long-range drive in the 60th minute and Sami lobbed the winner over keeper Eduardo 10 minutes later.
Benfica have the same points as Porto (27) after 11 matches but trail the league leaders on goal difference.
Arch-rivals Porto also made an early exit from the Portuguese Cup, the holders losing 3-0 at Academica in the previous round.
Sporting, the new favourites for the cup competition, play Belenenses on Monday.