Slimani netted in each half to hand Porto their first league defeat since Jan. 25 and extend his team's undefeated home sequence to 24 matches.
Jorge Jesus' side have led the way for much of the season but suffered a wobble before Christmas, falling to consecutive defeats to Braga in the Portuguese Cup and Uniao da Madeira in the league, allowing Porto to snatch first place.
Victory for Sporting gave them 38 points from 15 matches, two ahead of their opponents.
"We are in the lead now and we must learn how to defend it," Jesus told Sport TV.
Slimani opened the scoring in the 27th minute with his ninth league goal of the season, meeting Jefferson Nascimento's free kick with a bullet header that flew past keeper Iker Casillas.
Porto's Vincent Aboubakar was then denied an equaliser byan outstanding block from Rui Patricio but Sporting were comfortably the better side and Slimani's second ended the match as a contest.
The striker latched on to a sublime through ball from Bryan Ruiz in the 85th minute and fired a thumping effort in off Casillas' post.
"I'm convinced we can still win the title," said Porto coach
Julen Lopetegui. "We have more points than last year and have to back ourselves to come back and win many games."
Benfica kept pace with the top two after a 1-0 win at Vitoria de Guimaraes stretched their unbeaten run to eight games.
Youngster Renato Sanches scored in the 75th minute with a powerful angled drive from the corner of the box.
Benfica are third on 34 points, two behind Porto and eight ahead of fourth-placed Braga who drew 1-1 at Vitoria de Setubal.
(Writing by Ed Dove; Editing by Tony Jimenez)
