Leicester have now reached the quarters in four of their last five League Cup campaigns
Youri Tielemans and Ayoze Perez gave the Foxes a two-goal cushion by the break before Jamie Vardy added another.
Their sharpness was a step above and proved too much for third-tier MK Dons.
"We were hoping this could be a perfect game for us leading into the Premier League restarting and it turned out to be that," said Leicester assistant manager Chris Davies.
Thirty-eight days after the Foxes last played a competitive fixture, Brendan Rodgers' side did not look like a team who were lacking match-sharpness, and fired off early warning shots through Perez and Timothy Castagne.
Davies added: "It was a really good evening for us, really positive, having been a few weeks away now from competitive games, it was really good to get back with a good performance and a win.
"The cohesion was really good, we had the majority of the squad with us in our training camp [over the break]."
Both efforts missed the target but they soon found a way to beat the goalkeeper when Tielemans was on hand to fire home the opener after Jamie Cumming pushed an audacious Vardy backheel into the Belgian's path.
Leicester's second came when Perez produced a deft touch inside the 18-yard box to control a Luke Thomas long ball before slotting a composed effort into the back of the net.
The hosts struggled to make any impression and failed to capitalise on their best chance as Daniel Harvie blazed a half-volley over the bar shortly before the break.
Leicester's dominance grew after the break and Vardy made it three as he nodded in Castagne's dinked cross to complete the scoring in a one-sided victory.
The Foxes will be bolstered by the return of James Maddison when they take on Newcastle United on Boxing Day in their first Premier League game after the break, with the midfielder missing Tuesday's game.
Maddison was part of the England squad at the World Cup in Qatar but did not feature in any matches.
-- Courtesy of BBC Sport