Midfielders Oscar and Eden Hazard got the goals as Blues boss Jose Mourinho took the opportunity to give all 20 members of his squad some game-time against his former team at the Lucas Oil Stadium.
Oscar opened the scoring in the 13th minute with a fine curling right-foot shot, following an imposing run down the middle by Victor Moses.
Blues goalkeeper Petr Cech did well to keep out a deflected shot from Rodrigo Palacio eight minutes later, before Chelsea doubled their lead in the 29th minute.
Referee Ismail Elfath decided Moses had been fouled inside the area by Alvaro Pereira - a generous decision for Chelsea as the offence was committed outside the penalty box - and Hazard sent goalkeeper Samir Handanovic the wrong way from the spot.
Inter were reduced to 10 men in the 58th minute when Hugo Campagnaro was given a straight red card for a dangerous challenge on a grounded John Terry, who escaped injury and went on to complete the full 90 minutes.
Fernando Torres came on for the closing stages but the nearest he came to scoring was a left-foot shot from the edge of the area which was easily saved by Juan Pablo Carrizo, while another substitute Demba Ba brought a good save out of Carrizo 10 minutes from time.
Next up for Chelsea in the International Champions Cup are AC Milan, with the two teams meeting in New York's MetLife Stadium on Sunday.Mourinho's men start their Premier League campaign on August 18, with newly-promoted Hull the visitors to Stamford Bridge.