The Fire (9-6-4, 31 points) prevailed despite playing a man short for the final 21 minutes after defender Arne Friedrich was ejected with a second yellow card.
The Whitecaps (8-6-6, 30 points) suffered their second straight loss and third in a five-game road swing.
Chicago was awarded a free kick in the ninth minute when Whitecaps midfielder Jun Marques Davidson tripped Fire midfielder Patrick Nyarko on a run outside the box.
Pardo then lined a 23-yard kick into the right corner for his first goal of the season in the ninth minute.
An apparent second-half goal - a rebound shot by Dominic Oduru in front of the net in the 54th minute - was ruled offside.
Friedrich was ejected in the 69th minute and was given his second yellow card in two minutes after apparently tripping Vancouver forward Darren Mattocks.
Chicago goalie Sean Johnson had four saves, including one on a shot by Lee Young-Pyo that would have tied the game.
Chicago had back-to-back scoreless games and had not scored since June 29 on Marco Pappa's tally in the 58th minute of a 1-0 triumph at Sporting Kansas City.