Ishizaki was not to be denied a second time, however, and put the visitors in front with a header following a good team move.
Vancouver equalised after the break when Darren Mattocks picked up a loose ball and squeezed it into the net from a tight angle.
Robbie Keane put Los Angeles back in front after latching onto a knockdown from Rob Friend and slotting home.
Kekuta Manneh then levelled the score for the second time in the match when he curled an effort into the bottom corner.
Kenny Miller came close to finding a winner for the Whitecaps, but his effort flew just wide of the post.