James Maddison has scored 11 goals for Leicester this season, ending a run of six games without netting
Brendan Rodgers' men came into this knockout stage play-off round after finishing third in their Europa League group, but navigated the tie with few issues.
Holding a 4-1 lead from the first leg, it took Leicester just 100 seconds to extend their advantage as Harvey Barnes broke clear and curled a delightful finish into the far corner.
The England international could have added another in the second half but fired wide from an acute angle.
Compatriot Maddison then netted twice in the space of four minutes with a free-kick into the top corner and a sumptuous curling strike from 25 yards.
Randers did pull a goal back late on when Kasper Schmeichel's heavy touch on the ball allowed Stephen Odey to nip in and convert a gift from close range.
The draw for the Europa Conference League takes place on Friday when the Foxes will be picked out of the pot against a group winner.
After his side's Europa League exit at the hands of Napoli in December, boss Rodgers said he did not "even know" what the Europa Conference League was.
Now he does.
Uefa's newly-formed third club competition represents Leicester's only chance of claiming silverware this season after suffering a shock exit in the FA Cup, being knocked out of the Carabao Cup and lying in the bottom half of the Premier League.
Their overall form has been poor this season with Rodgers criticising his players' performance in the FA Cup loss at Championship side Nottingham Forest, though the side have not been helped by injuries to key players.
They will be glad to have faced Randers as their two victories in the last eight games in all competitions have been against the Danish outfit. The success also ended a run of four straight defeats away from home.
Though they were in a commanding position heading into the second leg, Rodgers still selected a strong side with mostly first-team regulars and the contest was ended courtesy of Barnes' coolly-taken goal.
It was a morale-boosting showing for Maddison and a decent performance was capped off by two well-taken goals in the second period.
Randers, who lie sixth in the Danish top flight, had numerous chances and, although Schmeichel made a stunning reflex save to deny Odey, the goalkeeper's blunder six minutes from time gave the home fans something to cheer on the night.
AZ Alkmaar (Ned), Basel (Swi), Copenhagen (Den), Feyenoord (Ned), Gent (Bel), LASK (Aut), Rennes (Fra), Roma (Ita).
-- Courtesy of BBC Sport