Former Inter midfielder Vieira was sent-off 21 minutes into the friendly at the M&T Bank Stadium in Baltimore in the early hours of Sunday morning GMT for an alleged elbow on Marco Materazzi .
From thereon-in City faced an uphill battle playing with ten men against the Champions League title holders.
Inter took the lead in the 39th minute when Obinna's shot took a deflection off substitute Micah Richards and beat Joe Hart in the City goal.
Inter made it 2-0 ten minutes into the second half when once again an Obinna cross was steered past substitute keeper Shay Given by Joleon Lescott.
A long range effort from Cristiano Biraghi in the 75th minute sealed a 3-0 win for Inter.
City: Hart (Given, h/t), Zabaleta, Kompany (Ireland, 80), Toure Kolo (Boyata, 62) , Bridge (Cunningham, h/t); Vieira, Toure Yaya (Lescott, h/t), Barry (Wright-Phillips, 55); Johnson, Jo (Richards, 30), Adebayor.
Inter Milan: Castellazzi, Zanetti, Cordoba, Materazzi, Chivu, Mariga, Cambiasso, Obi, Coutinho, Pandev, Obinna.
Attendance: 36,569.