The win sees Seattle move level on points with Colorado in the bottom half of the Western Conference.
Hendry Thomas missed with a couple of long-range efforts during the opening exchanges as Colorado looked to turn their possession into goals.
A minute later they took the lead through Martins, as the former Newcastle United striker found space in the area and fired the ball into the bottom corner.
Lamar Neagle almost doubled the lead immediately, but after being played in by Martins, he smashed his shot against the crossbar.
Atiba Harris missed two half-chances to level the match, either side of half time for the home side.
In the second period Colorado began to push even harder for an equaliser. Dillon Powers missed from just outside the box, before Harris struck the post with a looping header.
They struck the woodwork again 10 minutes from the end, when Kamani Hill somehow missed the target from six yards out.
Despite a scrappy end to the game, with Colorado having several free kicks in threatening positions, Seattle were able to hold on for all three points.