Brendan Rodgers' side have done remarkably well so far and the thrashing of Luton Town put more weight to their credentials.
Two goals each on either sides of the half helped the Foxes thrash Luton 4-0.
Meanwhile, Southampton also won after a commanding 4-0 win over Portsmouth.
Cedric Soares scored a brace.
Other major results of the night
Elsewhere, Everton shed off recent disappointments to beat Sheffield United 2-0. Watford saw Danny Welbeck score as the side held on to beat Swansea 2-1. Crawley Town stunned Stoke City 5-3 on penalties after a 1-1 draw earlier.