Goals from Oscar and Eden Hazard inspired the Premier League side to victory over the Nerazzurri, who had Hugo Campagnaro sent off in the second half in the first-ever football match played at Lucas Oil Stadium, home of NFL franchise the Indianapolis Colts.
Chelsea will now face AC Milan in New York on August 4, while Inter will do battle with La Liga's Valencia on the same day.
Jose Mourinho's men had been in lethal form in their previous five pre-season fixtures, scoring 14 goals and conceding just three, but it was the Portuguese manager's former employers Inter who came closest to breaking the deadlock early on Thursday.
Fredy Guarin unleashed a volley on goal after 10 minutes of play but the Colombian midfielder, who scored 10 goals despite a disappointing 2012-13 campaign for Inter, sent his stinging effort just wide of the post.
The Indianapolis crowd did not have to wait long for the opening goal, however, with Chelsea hitting the front just three minutes later.
Inter found themselves caught out in the attacking third and Chelsea took full advantage of a three-on-three situation, with Brazilian playmaker Oscar the beneficiary.
Walter Mazzarri's Inter side almost levelled proceedings seven minutes later but Rodrigo Palacio's long-range effort was tipped away for a corner by Petr Cech.
Chelsea were then awarded a controversial penalty in the 27th minute, which was converted by Belgian winger Hazard.
Replays showed Victor Moses had been brought down just outside the area but that did not faze Hazard, who doubled the lead from the spot.
The Blues ended the opening 45 minutes with a two-goal buffer and introduced the likes of Mark Schwarzer and Michael Essien after the break.
The substitutions added some fresh impetus around the pitch and they almost made it 3-0 early in the second half, but Romelu Lukaku's thunderous strike cannoned off the post.
Inter's task was made even tougher just minutes later, when Argentine defender Campagnaro was given his marching orders for a nasty tackle on Chelsea veteran John Terry.
Campanaro's dismissal took the sting out of the game, with Inter happy to sit back and avoid any further punishment.
Mourinho's men had chances to add some extra gloss to the scoreline through substitute Fernando Torres but he was unable to find the net.
The result saw the Europa League champions end their two-game losing streak on American soil, having lost twice to Manchester City in May.