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.
A frantic first half ended 2-2 after Maxim Tissot struck for the Impact in the 44th minute but Portland took the points at the Stade Saputo when Valeri scored with nine minutes remaining.
Montreal hit the front in the 13th minute when a rapid attack down the right saw Justin Mapp cross just behind Andres Romero but the Argentine striker did enough to collect possession, burst past his marker and then thrash the ball home.
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.
The win took the Timbers to 27 points - seventh in the West - only behind sixth-placed Los Angeles Galaxy on games won, while the fifth-placed Whitecaps have a one-point advantage after their draw on Sunday.
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.
But a penalty to Pedro Morales seven minutes into the second half was enough for Vancouver to claim a point in front of their home fans.
Dallas (30 points) sit fourth in the Western Conference standings.
