The hosts opened the scoring after just 10 minutes as Kekuta Manneh collected the ball on the left wing and cut inside. His first attempt smacked off the left post, but the ball came straight back in front of goal and Manneh stabbed it home on the second bite of the cherry for the early lead.
Nine minutes later Manneh got in behind the San Jose back line and was tripped by 'Quakes defender Victor Bernardez, resulting in a penalty kick which Morales calmly dispatched into the bottom left corner of the net.
Just moments later Morales completed his brace when he fired it past San Jose goalkeeper Jon Busch from outside the penalty area for a three-goal margin.
San Jose got back in the match just before the break when Alan Gordon was clattered in the penalty area by Whitecaps defender Jay DeMerit and referee Drew Fischer pointed to the spot.
Chris Wondolowski stepped up and buried it to pull the visitors within two at the intermission.
Wondolowski fired in his second of the match deep in stoppage time, but it wasn't enough for the 'Quakes and Vancouver held on to claim all three points.