Wondolowski paid for his miss in the 26th minute when the Galaxy took the lead through Landon Donovan as he latched onto Keane's through-ball and rounded San Jose keeper Jon Busch before slotting his shot into the net.
The visitors almost dragged themselves level when Wondolowski drilled a cross to the back post and Cordell Cato beat his man in the air but his header went just the wrong side of the post.
Los Angeles doubled their lead just before half time when Gyasi Zardes was brought down in the penalty area by Steven Beitshour.
Keane took the penalty and fired the ball through the hands of Busch who could done better to have kept the ball out.
After the break, the former Tottenham Hotspur man notched his second of the game and the Galaxy's third when he volleyed in from inside the penalty area after he was teed up by a lovely header from Sean Franklin.
Keane could have got his hat-trick when he collected Zardes's pass on the left and turned his man inside and out before firing a left-footed shot at goal, which went just wide of the post, as the Galaxy strolled to an easy win.