The result means that Vancouver Whitecaps will now advance to the playoffs instead.
Seattle made the breakthrough at CenturyLink Field in the 33rd minute from the penalty spot.
That lead lasted for just eight minutes, as Blas Perez smashed home the equaliser for Dallas four minutes from the half-time interval.
Seattle restored their one-goal advantage on the hour mark when Evans turned in Christian Tiffert's pass.
The hosts wrapped up the victory with 10 minutes left on the clock, Mauro Rosales tapping in Montero's pass with ease.