The 2011 and 2012 MLS Cup champions took the lead in the 38th minute when Swedish midfielder Stefan Ishizaki netted his second goal in three outings but the Whitecaps hit back in the 67th minute through Darren Mattocks.
Captain Robbie Keane had the Galaxy back in front with just over 10 minutes remaining when he fired home a left-footed volley but again conceded, this time allowing Kekuta Manneh to grab a leveller with four minutes of regular time left.
In the wake of the draw, which has the Galaxy sitting eighth on the Western Conference table, Keane spoke of the disappointment regarding a result he felt his side should have held on to.
"It feels like a loss to be honest with you," Keane told reporters.
"I don't see it as a draw; I see it as a loss.
"It's disappointing. You can't go up twice away from home and concede goals like that. The first goal was very, very sloppy.
“We had the momentum for most of the game; we kept the ball and kept it moving. We did well with both of our goals, but it feels like we have to score way more goals than everyone else, but that shouldn't be the case. We should be able to see games out."
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