The home side settled first in the game and Carlos Alvarez had the first effort at goal from just outside the box, but he could only blast his shot over the bar, under little pressure.
Chances were few and far between in the first half as the sides went into the break goalless.
Minutes later, Kennedy came to the home side's rescue again when he made an excellent block with his feet to deny a low effort from Wondolowski.
In the 80th minute the Earthquakes were reduced to 10 men when Steven Lenhart was sent off for a challenge on Kennedy as he went up for the ball and picked up his second yellow card of the game.
However, this was not to stop San Jose as they found a winner in the 87th minute despite their numerical disadvantage as Wondowlowski tapped in from close range after Kennedy fumbled Alan Gordon's shot from distance.