Tielemans decided the contest in the 63rd minute with a spectacular 30-yard strike into the top corner.
In the 87th minute, Chilwell also had a deflected goal overturned for offside after a VAR review.
The victory guarantees Leicester a place in the group stages of next season’s UEFA Europa League.
But Brendan Rodgers’ team are seeking a top-four finish for a UEFA Champions League spot and will look to stop Chelsea from leapfrogging above them into third when the two sides meet again at Stamford Bridge on Tuesday in the Premier League.
Leicester’s triumph means that unless they drop to sixth, which can only happen if West Ham United beat Brighton & Hove Albion later this evening, their UEFA group stage place by dint of the FA Cup will go to the next-highest ranked team in the Premier League not qualified for UEFA competitions.
This also means the UEFA Conference League spot awarded to the EFL Cup winners, PL champions Manchester City, will go to the team in seventh, or eighth if Chelsea finish outside the top four and beat Man City in the UEFA Champions League to retain a place in next season’s competition.