The Crew took a 1-0 lead in the 15th minute when Jairo Arrieta intercepted a clearing pass from Fire goalkeeper Sean Johnson and beat a sliding save try by defender Arne Friedrich for a tally.
But Chicago responded only 8 minutes later when Sherjill MacDonald hooked up with Rolfe with a through-pass and the Fire striker sent it home.
Rolfe struck again in the 26th, taking a pass from Patrick Nyarko and bending a shot past Andy Gruenebaum for the decisive score.
Chicago (16-8-5) used the victory to strengthen its hold on second place in the Eastern Conference.
Columbus (13-11-6) remained one point out of an playoff spot in the East.