Morales scored on a penalty kick in the 19th minute and kicked a shot in from about 20 yards out in the 20th minute.
''We got off to a great start,'' Morales said. ''The team played very well, it was very exciting for the fans and we created a lot of (scoring) opportunities.''
Kekuta Manneh also scored a goal and added an assist for Vancouver (3-2-4), which earned its first win in five games.
Chris Wondolowski scored both goals for San Jose (1-3-3) - in the 45th minute and in second-half stoppage time.
''We did not come out with a good mindset,'' Wondolowski said. ''Going down 3-0 against a very quality team, it's way too big a hole to climb out of. We didn't do things right.''
The Whitecaps had a goal disallowed in the 81st minute when Gershon Koffie was called for getting his hand on the ball just before he scored.
The game commemorated the first soccer contest between Vancouver and San Jose, which was played May 5, 1974, when both teams were part of the original North American Soccer League. Many fans wore 1970s-era clothing, including colorful bell-bottom pants, and donned long-haired wigs, fake handlebar moustaches and sunglasses.
''I challenged them at the start of the game because it was a fantastic occasion today for the club and the tradition of the club,'' Whitecaps coach Carl Robinson. ''I didn't want them to start slow where we have been in a few recent games.''
Manneh, who has been used mostly as a substitute, started in midfield in a move that paid off early when he gave the Whitecaps a 1-0 lead in the 10th minute. He took a shot off the near post and then put his own rebound in off the far post.
The goal came after Jay DeMerit checked the ball away from charging San Jose forward Yannick Djalo and sent the ball up the left flank. With Djalo injured in the process and kneeling on the turf, the Whitecaps were able to capitalize on an odd-man situation.
Djalo was replaced by Alan Gordon in the 14th minute.
''As soon as Yannick went down, they scored the first goal,'' Earthquakes coach Mark Watson said. ''It was just 10 minutes where we couldn't cope with them.''
Morales put the Whitecaps ahead 2-0 on a penalty kick nine minutes later after Darren Mattocks was deemed to have been taken down while deking with the ball in the San Jose box.
A minute later, Morales notched his second goal as he put a shot into the same corner from just outside the top of the San Jose box. After scoring, Morales took off his jersey, waved it over his head and ran bare-chested to the bench - only to get an automatic caution for excessive celebration. Morales put his shirt back on and referee Drew Fischer pulled out his yellow card.
Vancouver lost Mattocks in the 30th minute after he pulled up lame while chasing a loose ball down the left flank. He was replaced by Erik Hurtado.
''(The late rally) was too little, too late,'' Wondolowski said. ''We can't be doing that. This loss is unacceptable.''