The Toffees, meanwhile, remain in the bottom three with just eight points in 10 games and David Unsworth will have to do a lot more if he is to land the job on a permanent basis, following his appointment as interim manager after Ronald Koeman was sacked last week.
The former Everton defender rang the changes for his first game as Premier League manager, with forgotten men Kevin Mirallas and Aaron Landed handed a rare start, while summer signings Gylfi Sigurdsson and Davy Klaasen were benched and dropped altogether respectively.
Hopes of a fresh start for Everton, however, had all but evaporated within half-an-hour, while Puel could have hardly hoped for a better start to his tenure. Leicester's opener was strikingly reminiscent of their football under Claudio Ranieri, as Demarai Gray picked up the ball just outside his own box following an Everton free-kick and drove forward, beating Tom Davies and Idrissa Gueye before finding Riyad Mahrez.
The Algerian's firs-time cross was swept home by Jamie Vardy, who scored his first goal in four games.
Everton should have been level 10 minutes later, after Dominic Calvert-Lewin failed to get on the end of Lennon's cross when any sort of touch would have got Everton level. The mistake proved costly as Leicester added a second only a few minutes later, when Everton right-back Jonjoe Kenny swung his boot at the ball in an attempt to clear Gray's cross, only to catastrophically sliced it behind him and into his own net.
The visitors were then left aggrieved soon afterward, when Lennon was brought down in the box by a rash challenge from Christian Fuchs. The Leicester defender clearly took Lennon's legs and none of the ball, but what had looked a clear foul to most inside the ground was not deemed worthy of a penalty by Andre Marriner nor by his assistant.
Leicester controlled the second half with relative ease, while Everton failed to trouble Kasper Schmeichel and there was almost a feeling of inevitability as they suffered their fifth defeat in six games in all competitions.
Everton's £140m spending spree was suppose to prove the catalyst for a change and while Champions League aspirations sounded perhaps a tad too lofty, few would have imagined Everton to be in a relegation battle by the time the clocks went back.
All square on the south coast
Meanwhile, in Sunday's early kick off, Glenn Murray's third goal in two games saw Brighton come from behind to rescue a point against Southampton and extend their unbeaten run in the Premier League to four games.
In the first meeting between the two sides in seven years, the visitors took an early lead after a free-kick from James Ward-Prowse cannoned off the crossbar and into the path of Saints captain Steven Davis, who headed in the rebound.
The goal, only the third Southampton have scored away from home in the league this season, seemed to stir Brighton into life. However, despite enjoying the lion's share of possession, the hosts failed to trouble Southampton until early in the second half, when Murray headed Pascal Gross' cross past Fraser Forster to draw his side level.
While Brighton deserved the equaliser, the England international would feel he should have kept Murray's header out, as it appeared to loop past his outstretched arm almost in slow motion. The result leaves Southampton in ninth place, while Brighton are a point behind in 12th spot.
"I think a draw in the end was probably a fair result," Brighton manager Chris Hughton told Sky Sports.
"It would've been an injustice if we'd lost the game and we deserved to get back into it."
His counterpart, Mauricio Pellegrino, added: "It was a really tight game. It was high tempo, up and down all the time. We never could control the ball totally and create more action because both teams were really compact and there were not too many spaces to think about.