Chara got his right foot on the end of a cross from Jorge Villafana on 61 minutes, producing the only goal of a back-and-forth match.
The result moved the Timbers from third place to first in Major League Soccer's Western Conference. Portland, with an MLS-leading 45 goals this season, has already clinched a playoff position.
The match was more important to the Whitecaps, who needed at least a point to keep pace for a lower playoff spot. Instead, the loss sent them into 10th place with only one match to play and their chances of getting into the top eight slim.
The Whitecaps pressed for an equalizer late on, knowing they needed at least a point from the match.
A yellow card for the Whitecaps midfielder Michael Baldisimo means he will miss the next game.
Portland had to scramble in the final couple of minutes, as captain Diego Valeri went down, along with forward Jaroslaw Niezgoda. The Timbers had to make two quick substitutions to play out approximately the last four minutes of the game.