The home side took the lead on eight minutes when Erik Lamela converted at the back post after the visitors had failed to clear their lines.
Francesco Totti nearly doubled Roma's advantage early in the second half, but his free kick came back off the crossbar.
It was Parma's turn to hit the crossbar on 62 minutes as Gabriel Paletta's header from a corner rattled the woodwork.
Having hit the bar with his earlier free kick, Totti made no mistake in the 72nd minute as his powerful strike found the net.
The goal was a significant one for the veteran as it took him to second place in the all-time top scorers' list in Serie A history.