Maritimo made the trip across Funchal hoping to build upon the 4-0 thrashing of Boavista in their previous outing, though they came unstuck against their rivals.
The scalp of Boavista ended a run of four successive league defeats for Maritimo and, although they remained level until half-time, the second half belonged to Manuel Machado's men.
Just a few moments after Danilo hit the post from a Maritimo corner, half-time substitute Willyan broke the deadlock, stroking home from inside the area.
The hosts' second arrived with 74 minutes on the clock as Patrick Bauer brought down Marco Matias in the penalty area, allowing the Portuguese forward to bury the resulting spot-kick.
Matias doubled his tally with four minutes to go, scoring his fifth goal of the season, exactly half of Nacional's total in the Primeira Liga this term.
The result leaves Martimo 10th in the table, while Nacional leap up to 13th, moving five points clear of second-from-bottom Penafiel in the drop zone.