The visitors threatened early in the game when Servando Carrasco lifted a dangerous cross to the back post for Will Bruin, who powered a header at goal, but Jon Busch made a good stop to keep his effort out.
The ball was played to Stephenson, who blasted an effort through a crowd of Houston players on the line to find the net.
After the break, the Earthquakes were handed the chance to double their lead when Steven Lenhart was fouled in the box by Corey Ashe. Stephenson took the spot kick and found the net, sending Hall the wrong way.
The home side almost got a third goal when a free kick was lifted into the box and Lenhart headed at goal only to see his effort hit the bar, and from the rebound he blasted over.
However, San Jose did find a third goal to secure their win when Hall misjudged the flight of the ball and allowed Atiba Harris to nip in and find the net after his initial effort hit the post.