Henrique Calisto's side went into the game at the Estadio da Madeira on the back of successive top-flight losses, and fell behind after just 20 minutes when Nacional forward Candeias scored from the penalty spot.
Tiago Valente equalised six minutes after the restart as Pacos went in search of just their fifth away point of the season.
However, they were level for just 11 minutes, as Diego Barcellos struck the winner for Nacional just after the hour to end their run of five games without a victory.
In Monday's other fixture, Estoril closed the gap on third-placed Benfica to seven points with a routine 2-0 success over Gil Vicente.
Brazilian midfielder Evandro opened the scoring for the hosts midway through the first half, before substitute Diego Amado sealed the three points four minutes from time.
The result gives Estoril their first win at the Estadio Antonio Coimbra da Mota since the opening day of the season and extends Gil Vicente's run without a victory to four games.
