Everton started well and made the breakthrough in the 12th minute of the contest, as Ndiaye's low strike touched the inside of the post before nestling in the bottom corner.
The Toffees were dominant at a rainy King Power Stadium, but a leveller for Leicester almost arrived in the latter stages of the first period when Mavididi's cross headed towards goal, only for Toffees goalkeeper Jordan Pickford to palm the effort onto the crossbar.
Everton had 10 shots in the opening half of action to Leicester's three, and the home side were left with much to ponder heading into the half-time break in front of their own supporters.
Kickoff in the second period was delayed due to the bad weather, but the rain was still hammering down, with Everton coping better with the extreme conditions.
Leicester managed to level the scores in the 73rd minute, though, with Mavididi bundling the ball home from close range after Everton were unable to deal with a corner.
Everton have moved off the bottom of the Premier League table courtesy of their first point of the season, while Leicester remain 15th, boasting three points from their first five games.
LEICESTER VS. EVERTON HIGHLIGHTS
12th min: Leicester 0-1 Everton (Iliman Ndiaye)
Everton take the lead in the 12th minute of the contest, and it is a first Premier League goal for the Toffees for Ndiaye, who shows excellent footwork inside the penalty box before scoring via the post.
Brilliant goal from the summer arrival at Goodison Park.
73rd min: Leicester 1-1 Everton (Stephy Mavididi)
Leicester finally level the scores in the 73rd minute of the contest, and the goal comes from Mavididi, who fires home from close range after Everton had failed to deal with a corner.
MAN OF THE MATCH - ILIMAN NDIAYE
Ndiaye thrived during his previous spell in England with Sheffield United, notably hitting 14 Championship goals during the 2022-23 campaign, and he has started well at Everton.
The 24-year-old's excellent goal made the breakthrough at the King Power Stadium, while he finished with a pass success rate of 89%.
Ndiaye was the obvious threat for Everton in the final third of the field, but he was also more than prepared to help his side out from a defensive point of view, with the Senegal international the standout player on the field.
LEICESTER VS. EVERTON MATCH STATS
Possession: Leicester 58%-42% Everton
Shots: Leicester 12-16 Everton
Shots on target: Leicester 2-5 Everton
Corners: Leicester 6-1 Everton
Fouls: Leicester 11-12 Everton
WHAT NEXT?
Leicester's attention will now switch to the EFL Cup, preparing to face Walsall in the third round of the competition on Tuesday night, before heading to Arsenal in the league next Saturday.
Everton, meanwhile, lost on penalties to Southampton in the EFL Cup last week, so the Toffees will not be back in action until a home league fixture with Crystal Palace next Saturday.