Inter broke a scoreless tie just moments before halftime. On a free kick from the left outside of the box, Dodo's left-footed service found Vedic at the center of the penalty box and his deflected header ticked off the fingertips of goalkeeper Lukasz Skorupski into the upper right corner.
Roma almost tied it in the 48th minute, but Mattia Destro's header barely missed. Nagatomo provided insurance in the 69th minute as he collected a loose ball in the right side of the box and buried it past Skorupski in the top right corner.
Inter finished its group games in the exhibition International Champions Cup with six points, two behind Manchester United. The final is Aug. 4.