Leonardo Jardim's men fell behind in the Primeira Liga clash eight minutes before the break when Rafa Silva's low effort deflected off the post and goalkeeper Rui Patricio and into the net.
However, the hosts levelled after 71 minutes as Jefferson converted from the spot following Vincent Sasso's foul on Carlos Mane.
From there all the momentum was with the capital club, who made sure of the points four minutes later with Slimani's sixth of the season.
The Algeria international's half-volley from the edge of the area took a wicked deflection over a stranded Eduardo to spark joyous scenes at Estadio Jose Alvalade and mark the second time in as many games that Jardim's side have come from behind to win after doing the same at Rio Ave last week.
Relegation-threatened Olhanense's day got worse two minutes from time when substitute defender Mario Sampirisi was dismissed for a foul on Ricardo Vaz, who slotted away the resulting penalty with aplomb.
