Marcos Alonso stepped up to provide the two killer blows against the Foxes, opening the scoring after Eden Hazard found him with a clever pass in the sixth minute and he soon doubled the lead with a shot from the edge of the box which deflected off Wes Morgan and squirmed past Kasper Schmeichel.
Pedro killed off the game after Willian found him with a cross - as he nodded home into an open net - but all the talk was about the money, power and Costa at the King Power Stadium.
Chelsea adapted well with Hazard playing as a false nine and strolled past the Premier League champions with ease, despite Costa missing out from what Chelsea officially stated was an injury.
Costa will have been watching on at home and will have learned that Chelsea are capable of moving on without him, even though he has 14 league goals to his name, so far this season.
Ideally, Chelsea would like to bring back Costa, but Conte will want to make an example that a bid from China doesn't entitle his players to bumper pay rises. Costa's row came after he and the club had negotiations before he received an offer of £30 million from a club thought to be Chinese Super League outfit Tianjin Quanjian.
There is no news on when Costa might return for Chelsea after he trained alone this week following the falling out, but they proved that they can cope without him, at least in the short term.
Chelsea have goals all over the pitch and Hazard is ready to step up with Michy Batshuayi waiting patiently for his chance on the bench. Alonso proved today that he can be one of the many who can provide goals, but Pedro, Willian and Victor Moses were all threats that the Leicester side couldn't handle.
Conte had to fight to keep Costa last summer and he is having to deal with yet more unrest from his forward in the following transfer window - with the Spain international's head turned by Atletico Madrid prior to the 2016-17 campaign.
All clubs have patience for their biggest stars no matter what they do, but Costa will need to be wary that if he pushes Conte too much that he might just give him what he wants - a hand opening the exit door.
In both of Chelsea's games without Costa, they have recorded 3-0 wins after their last victory over Bournemouth. Willian, Pedro and Hazard have proven that their link up play can be devastating enough to provide goals in the absence of the club's true out-and-out striker.
Morgan and Robert Huth couldn't deal with the movement of the three forwards and Conte will trust his alternative approach to his striker issues.
Chelsea's win over Leicester was another statement that this is a club ready to be champions, but Conte's job will be much easier with a motivated Costa than without one. If the worst came to the worst, then the west Londoners have proven that they can get wins without Costa and that they have more than one superstar in their squad.
Cesc Fabregas and Batshuayi came off the bench in the latter stages which also displays the remarkable depth of the champions who remain in good health as they chase their title, amidst controversy.
Chelsea's victory worked as an advert for Costa showing exactly why he should stay at Stamford Bridge as he has the chance to help write another remarkable chapter in his club's history.