The buildup was overshadowed by Serge Gnabry testing positive for the coronavirus on Tuesday after he had taken part in the team's final training session for the game.
Rashford, who scored the winning spot-kick when United knocked PSG out in 2019, drilled home a low shot three minutes from the end which won a thrilling Group H contest at a near-empty Parc des Princes.
Barcelona had its first defeat under Ronald Koeman when it lost 1-0 at Getafe on Saturday, right after Madrid was beaten 1-0 at home by recently promoted Cádiz