Sporting's win, which heaped on the misery for their third-placed opponents, kept the Lions two points behind leaders Benfica, their neighbours who beat Vitoria Guimaraes 1-0 on Friday, with two matches each to play.
"The doubts about who will be the champions persist, but nobody has any doubts about which is the best team, it's Sporting," said their coach Jorge Jesus, in typically feisty mood.
Benfica have 82 points from 32 games, with Sporting on 80 and Porto a distant third on 67. Sporting, who last won a league game at Porto nine years ago, went ahead with a superbly executed goal in the 23rd minute.
Joao Mario controlled a difficult ball on his chest, beat two defenders and delivered a low cross which Algerian international Slimani clinically turned in at the near post. Hector Herrera, who hit the post in the seventh minute, equalised with a penalty in the 35th minute, only for Slimani to head Sporting back in front from Bryan Ruiz's cross one minute before halftime. Bruno Cesar wrapped up the three points for Sporting five minutes from time with a shot which Iker Casillas seemed to have covered but allowed to slip under him.
(Writing by Brian Homewood, editing by Ian Chadband)
