Torres settled a deflected shot inside the penalty area and, with his back to the goal, sent a volley to the top right corner.
The late goal gave Chivas USA (5-7-5) its first three-game winning streak of the season — all shutouts.
It was Torres' 12th goal of the season, leaving him two goals behind New York's Bradley Wright-Phillips for the MLS lead.
The Impact (3-8-5) is the only team in the MLS without a road victory.
Montreal's Andres Romero had an open shot outside the six-yard box in the 66th minute, but his left-footed attempt was stopped by goalkeeper Dan Kennedy.
U.S. goalkeeper Tim Howard attended the game.