Leicester sit top of Group G with six points after Slimani headed powerfully home from a Riyad Mahrez cross in the first half for his sixth goal in his last four matches against Porto, having joined Leicester from Sporting Lisbon in August.
It was the first time Leicester had tasted Champions League football at home and they came into the game on the back of a 4-1 defeat to Manchester United and a run of poor form in the Premier League, but they looked comfortable throughout against Porto.
The visitors, who have one point from their opening two group games, did manage to rattle the post late on through Jesus Corona, but they were unable to exert sufficient pressure as they failed to win for the 17th time in England.
"We played with our spirit tonight," Leicester boss Claudio Ranieri said as his team stayed two points clear of FC Copenhagen at the top of the group.
"The last pass wasn't always there, but Riyad Mahrez made one fantastic pass for Slimani."
Leicester may be Champions League novices but in Slimani, the English side had a player who knew their experienced Portuguese opponents well and had enjoyed remarkable success against them.
He was signed from their rivals Sporting having scored freely against Porto in recent meetings and he was causing them trouble soon after kick off at the King Power stadium.
The Algerian served warning when he headed a Marc Albrighton free kick straight at Porto keeper Iker Casillas after 11 minutes but he was more clinical 14 minutes later.
Mahrez controlled a cross-field pass superbly, before shifting the ball out of his feet and curling a perfect cross into the path of Slimani who launched himself in front of the defender to head home.
It was his third goal in four games for Leicester, all of which have been headers.
Porto, who had looked sprightly in the opening minutes, seemed deflated, although a curling free kick from Miguel Layun that drifted just wide came close to levelling the encounter 10 minutes before halftime.
There were few real chances after the break with Mahrez having an early effort pushed wide by Casillas before Porto began to exert some pressure late on as Leicester sat back and sought to hit them on the counter.
Despite having a lot of the ball, Porto created little until the 84th minute when a rifled effort from substitute Corona was deflected against the post and away to safety.
(Reporting by Toby Davis in London,; editing by Pritha Sarkar and Ian Chadband)
