The Algerian striker continued his remarkable scoring record this year versus The Dragons, scoring his sixth goal in four outings against the Portuguese outfit.
The Foxes held off a late surge by the visitors to top the group after two games. It is the perfect response, bouncing back after a 4-1 defeat to Manchester United in the Premier League last weekend.
'Dragon-Slayer' opens scoring
After a lively start by both sides, the hosts finally lit the blue touch paper in the 25th minute. After neat work from Marc Albrighton, his cross-field ball found the lurking Riyad Mahrez on the right.
The Algerian then whipped in a trademark looping cross to by-pass the Porto defence and find the head of compatriot Slimani. The striker has now scored six times against Dragões this calendar year, with five for former club rivals Sporting Lisbon.
The hosts came close to doubling their lead through Robert Huth via a set-piece. The closest Porto came to levelling proceedings was from a Miguel Láyun free-kick that skimmed a a yard wide of Kaspar Schmeichel's goal. The hosts took a 1-0 lead into the break.
Foxes sniff a second
Into the second period, Claudio Ranieri's men looked the more likely to double their lead. Again it was the elusive Mahrez who was creating panic in the Porto defence. The visitors were reduced to set-piece creation, as left-back Alex Telles blazed over from just outside the D.
The Algerian then nearly did double the lead for Ranieri's men. Set up again by neat play around the area, Mahrez was again in the pocket and struck from 25 yards, which Porto 'keeper Iker Casillas was forced to turn behind.
Just after the hour mark, the Portuguese side made a double change and it was substitute Hector Herrera who forced a smart save from Schmeichel, to divert the Mexican's swerving half-volley. Porto were upping the tempo into the last quarter of an hour.
Dragons' flame extinguished as hosts hold on
As Porto threw on their third defender, boss Nuno sensed a late equaliser. Jesus Corona the third change gave the visitors a sudden injection of swagger. First the Mexican lofted a ball over the Leicester defence, but Andre Silva could not take the ball under control.
Then with nine minutes to go, Corona himself came closest for The Dragons. A floated ball came the way of the Mexican who clattered a volley - taking a nick off Albrighton - and off the face of the post.
The hosts survived a nervy last few minutes to record their second-successive Champions League win in their debut season, topping Group G with six points.