Villa had the better of the first half, producing the first chance of the game when John McGinn curled just over.
Ollie Watkins was then ruing his luck again after missing two big chances against Arsenal last week, as his close-range shot was saved by Mads Hermansen.
The visitors finally found the breakthrough via a clever set-piece, with Onana sliding in at the back post for his second goal this season.
Jacob Ramsey, who drilled the ball across to Onana, could have then doubled Villa’s lead, but Hermansen parried his effort.
Leicester improved later in the half as Caleb Okoli chested towards goal, but Emiliano Martínez kept his clean sheet intact before HT.
The Foxes carried their momentum into the second period, as Okoli fired just over from distance before Jamie Vardy had the ball in the net, only to be denied by the offside flag.
However, it was Villa who found the net minutes later, and this one counted as Durán headed home his second goal as a substitute already this season.
The Villans looked to be cruising to victory, but Facundo Buonanotte volleyed home his first goal for Leicester to keep the match interesting.
Durán could have put the game to bed late on though, but his shot could only find the goalkeeper’s gloves after a sharp turn.
Nonetheless, despite now going eight league matches without a clean sheet, Unai Emery’s side still managed to hold on for victory.
Meanwhile, Steve Cooper now has an unwanted record of being the first Leicester manager since Paulo Sousa in 2010 to fail to win any of his first three league games.
Flashscore Man of the Match: Jhon Durán (Aston Villa)
