The visitors, coached by ex-Chelsea boss Claudio Ranieri, only gained promotion from the second tier at the end of last term but many have forecast great things this season on the back of a summer spending spree, including striker Radamel Falcao.
And the 27-year-old Colombian, signed for a reported £50m, got on the scoresheet in a lively and entertaining contest on Saturday afternoon at the King Power Stadium.
It was, though, the Foxes that began brightly, with Danny Drinkwater forging forward to set up Matty James, whose shot was tipped brilliantly around the post by Danijel Subasic.
The visitors hit back and soon found the net after a corner by midfielder Joao Moutinho, another recent acquisition for £21.5m from Porto, finding the head of defender Layvin Kurzawa.
A long-range effort by Chris Wood came close to an equaliser, but as the interval loomed Falcao was rewarded for his first-half efforts, tapping in Andrea Raggi's low cross.
Anthony Knockaert's deflected shot was a useful effort for Nigel Pearson's side, but the Foxes continued to struggle in possession as Monaco introduced James Rodriguez and Jakob Poulsen from the bench.
Summer signing Zoumana Bakayogo was brought on in the 77th minute to make his Leicester debut, only for the dominant French outfit to step up another gear.
Marcel Tisserand raced clear of the sleepy defence (86) and produced a cute finish to seal the victory.