Brendan Rodgers' men came into this knockout stage play-off round subsequent to completing third in their Europa League bunch, however explored the bind with not many issues.
Holding a 4-1 lead from the principal leg, it took Leicester only 100 seconds to expand their benefit as Harvey Barnes broke clear and twisted a great completion into the furthest corner.
The England worldwide might have added one more in the final part however terminated wide from an intense point.
Comrade Maddison then, at that point, got two times over the course of about four minutes with a free-kick into the top corner and a rich twisting strike from 25 yards.
Randers pulled an objective back late on when Kasper Schmeichel's weighty touch ready permitted Stephen Odey to nip in and convert a gift from short proximity.
The draw for the Europa Conference League happens on Friday when the Foxes will be selected from the pot against a gathering victor.
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Harder tests to come for Foxes
After his side's Europa League exit on account of Napoli in December, manager Rodgers said he didn't "know" what the Europa Conference League was.
Presently he does.
Uefa's recently framed third club rivalry addresses Leicester's just possibility guaranteeing flatware this season in the wake of experiencing a shock exit in the FA Cup, being taken out of the Carabao Cup and lying in the base portion of the Premier League.
Their general structure has been unfortunate this season with Rodgers censuring his players' presentation in the FA Cup misfortune at Championship side Nottingham Forest, however the side have not been helped by wounds to vital participants.
They will love to have confronted Randers as their two triumphs in the last eight games in all contests have been against the Danish outfit. The achievement likewise finished a run of four straight losses from home.
However they were in an ordering position heading into the subsequent leg, Rodgers actually chose a solid side with generally first-group regulars and the challenge was finished politeness of Barnes' coolly-taken objective.
It was an assurance helping appearing for Maddison and a respectable exhibition was covered off by two very much taken objectives in the subsequent period.
Randers, who lie 6th in the Danish first class, got various opportunities and, despite the fact that Schmeichel made a staggering reflex save to deny Odey, the goalkeeper's botch a little ways from time gave the home fans something to applaud the evening.
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