Nonetheless, Claude Puel's side were able to hold out for a clean sheet and all three points against a dangerous Wolves side that hit the woodwork three times during the game.
The visitors began brightly and came within a whisker of taking the lead just three minutes into the game, but Joao Moutinho's ferocious effort bounced off the crossbar.
Leicester struggled to contain their opponents at first and, following a calm period, had the woodwork to thank once again as Raul Jimenez struck from the edge of the area on 22 minutes.
However, Wolves found themselves cursing their luck when, seven minutes later, Marc Albrighton's delivery came off the head of Conor Coady before being accidentally thumped into the back of the net by Doherty.
The Foxes then added a second just before the break as Mike Dean played the advantage following a Ricardo Pereira foul, which allowed Maddison to collect the loose ball and drill into the bottom right-hand corner of the net.
Vardy's sending-off on 66 minutes, which came following a reckless studs-up tackle on the back of Doherty's leg, generated some anxiety among the home faithful, but Wolves could not make their man advantage count come the final whistle.
LEICESTER CITY (4-2-3-1): Schmeichel; Pereira, Evans, Maguire, Chilwell; Mendy, Ndidi; Albrighton (Amartey 60'), Maddison (Silva 82'), Gray (Iheanacho 82'); Vardy
WOLVERHAMPTON WANDERERS (3-4-2-1): Patricio; Bennett, Coady, Boly; Doherty (Gibbs-White 69'), Moutinho, Neves, Jonny; Costa (Traore 45'), Jota (Bonatini 45'); Jimenez
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