Chelsea play Premier League rival Arsenal in Dublin Wednesday before wrapping up their pre-season campaign at home to Lyon on August 7
Chelsea beat Inter Milan 5-4 on penalties as goalkeeper Willy Caballero saved from Milan Skriniar in the shootout following a 1-1 draw in their opening game of the International Champions Cup.
Spain international Pedro struck after just eight minutes in Nice, slotting in a rebound after Inter keeper Samir Handanovic saved from a lively Alvaro Morata.
It was a second goal in as many games for Pedro, who celebrated his 31st birthday Saturday, after he netted the winner in Monday's 1-0 victory over Perth Glory in Australia.
Inter levelled early in the second half through Roberto Gagliardini, whose drilled shot proved too much for Argentina's Caballero after fellow half-time substitute Tiemoue Bakayoko gave the ball away.
New Chelsea signing Jorginho nearly won it with a curling effort that forced Handanovic into a fine sprawling stop, while Tammy Abraham couldn't hit the target as he tried to steer home an Emerson cross.
Twenty-year-old Argentine Lautaro Martinez, who joined Inter from Racing Club at the start of July, almost snatched a winner for the Italians in stoppage time when his sharp first-time strike was well kept out by Caballero.
Caballero, who was dropped at the World Cup following a 3-0 group stage loss to Croatia, saved from Skriniar with his legs in the shootout before Cesar Azpilicueta converted the decisive spot-kick.
Chelsea play Premier League rival Arsenal in Dublin Wednesday before wrapping up their pre-season campaign at home to Lyon on August 7, two days after facing Manchester City in the Community Shield.