San Jose almost took the lead when Leandro Barrera weaved his way into the box, but he lost his composure at the vital moment and skewed his shot wide of the post.
The Earthquakes came within inches of going ahead minutes later when Mark Sherrod powered a header at goal from a corner, but Powell was on hand to clear the ball off the line.
Dairon Asprilla sparked Portland back into life when he raided forward and drilled an effort at goal from distance, only to see his strike sail just over the bar.
In the second half, Diego Valeri almost unlocked the San Jose defence when he weaved his way towards goal, but his strike was saved by Bingham.
The Timbers thought they had taken the lead in the 87th minute as Powell released the run of Gaston Fernandez who slotted the ball past Bingham, but the goal was ruled out for offside.
However, the home side were not to be denied as Jewsbury fired home the winner in the dying seconds, pouncing on a loose ball in the penalty area to find the net.