The Timbers claimed their second straight win to maintain pressure on the teams immediately above them in the Western Conference, including Vancouver Whitecaps, who were held to a 2-2 draw at home by FC Dallas.
In Montreal, the hosts were unable to end their losing streak, which stretched to five matches, despite scoring the first goal of the game.
The Impact had the ball in the back of the net again in the 22nd minute but Jack McInerney's effort was ruled out correctly for offside before the Timbers started to gain the ascendency.
The visitors eventually equalised with 11 minutes left in the half when Darlington Nagbe's reverse pass found Max Urruti in a pocket of space and the striker toe-poked his shot past Montreal goalkeeper Evan Bush.
Portland hit the front five minutes later after Valeri was tripped in the box by Montreal captain Patrice Bernier, with the Timbers' skipper Will Johnson making no mistake from the spot.
But contest was level at half-time thanks to Tissot's strike just before the break, with the 22-year-old finishing off a nice cutback from Bernier.
Portland would emerge victorious, however, with Valeri finishing from the edge of the box in the 81st minute after Rodney Wallace's cross was cleared only as far as the Argentine playmaker.
Vancouver trailed 2-1 at half-time after Blas Perez and Michel's goals for Dallas had overcome Darren Mattocks' early strike for the Whitecaps.
