Nalbandian, the former world No. 3, dispatched Ram 6-4, 6-0, converting on the only break point of the opening set and losing just eight points total in the second set.
Nalbandian saw his first ATP Tour action following May hip surgery. He made his return last month in the Davis Cup semi-finals, winning two singles matches against Russian opponents.
American Ryan Sweeting thwarted James Blake's attempt to regain a Top 100 ranking by notching a 3-6, 6-3, 6-4 victory in another first-round Legg Mason match.
Serbian Viktor Troicki earned a second-round matchup with American Mardy Fish after easily downing Kevin Kim 6-1, 6-2 in 57 minutes.
Uzbekistani Denis Istomin needed 2 hours, 27 minutes, to prevail over Argentine Leonardo Mayer 6-4, 5-7, 7-6 to move on to the second round.