The home side played most of the match down a man after Agustin Pelletieri received a straight red card in the 13th minute for a poor challenge on Vancouver's Pedro Morales.
But Chivas managed to take the lead on the stroke of halftime through Erick Torres, only for Manneh to salvage a point for his team nine minutes from time.
After a resounding 4-1 win over Red Bull New York to open the season, a lot more was expected from the Whitecaps on Sunday as the team managed just two shots on goal against a 10-man side.
Pelletieri's dismissal was the first real incident in the match as both sides started slowly, but Vancouver failed to get going despite the numerical advantage and went behind after a turnover from Nigel Reo-Coker.
Mauro Rosales stole the ball from Reo-Coker and fed a pass to Torres, whose shot took a wicked deflection off of Vancouver defender Jay DeMerit before finding the back of the net.
The Whitecaps didn't manage a shot on target in the first half but Manneh spiced up the attack when he entered the contest in the second half, and he nearly found the net in the 75th minute with a shot that sailed just past the top corner.
But Chivas couldn't hold the lead and a giveaway by Dani Fragoso led to the equalizer with Darren Mattocks doing good work to set up Manneh for a simple finish.
Chivas had one final chance to steal an unlikely win in the 85th, but Vancouver goalkeeper David Ousted made a fine stop on a header from Torres.