The Algeria international moved to Leicester from Sporting CP last month and his decisive first-half header at the King Power Stadium on Tuesday took his tally to six goals in four games against Porto in 2016.
Slimani netted braces in the two Primeira Liga meetings last season, and scored again in a 2-1 win at the start of the campaign before completing his club-record switch to the Premier League champions.
This goal – his third in two home matches after a brace of headers against Burnley 10 days ago – sees the Foxes sitting top of Group G with maximum points ahead of the visit of second-placed Copenhagen in three weeks.
Once again, it was an impressive response in Europe from Claudio Ranieri’s men, who put Saturday’s 4-1 reverse at Manchester United firmly behind them having won 3-0 at Club Brugge on matchday one immediately after a 4-1 humbling at Liverpool.
Porto, meanwhile, were lacking a cutting edge for the most part, although they almost snatched an undeserved point seven minutes from time when substitute Jesus Corona thumped a deflected volley against the upright.
A lively opening saw nervy moments for both goalkeepers – the returning Kasper Schmeichel rushing from his box before gratefully seeing Andre Silva’s lobbed attempt drop wide of the target.
Schmeichel’s opposite number Iker Casillas – a three-time winner of this competition with Real Madrid – flapped under a Christian Fuchs long throw and then comfortably held Slimani’s header from Marc Albrighton’s set-piece delivery.
Riyad Mahrez had been a peripheral figure, but he was heavily involved in Leicester’s opener in the 25th minute.
Albrighton’s raking pass picked out the Algerian on the right, and his pinpoint cross into the six-yard box was buried by his international team-mate Slimani with a flying header.
Porto went agonisingly close to an equaliser 10 minutes later as Miguel Layun’s free-kick clipped the side-netting, but that represented a rare threat from the visitors in the first half.
By contrast, Leicester continued to look dangerous and Casillas saved well from Mahrez’s low drive just prior to the hour.
There was a late scare as Corona crashed his effort against the upright with Schmeichel motionless, but the hosts held on under mounting pressure to seal the points