The Galaxy, featuring former England midfielder David Beckham and Ireland striker Robbie Keane, had to come from behind though to beat the first Canadian team to feature in the MLS post-season.
The Whitecaps, in just their second season in MLS, grabbed the lead in the fourth minute when Jamaican Darren Mattocks coolly finished after Matt Watson had broken down the left flank and pulled the ball back into his path.
Beckham went close to an equaliser on the stroke of half-time with a trademark curling free-kick that Vancouver keeper Brad Knighton superbly tipped wide.
The Whitecaps could have doubled their lead in the 68th minute when Scottish forward Kenny Miller forced a save out of Josh Saunders and Barry Robson was unable to make the most of the loose ball.
Within a minute though, L.A were level - Beckham took a short corner to Juninho, whose cross was superbly hooked home by Mike Magee.
Vancouver lost central defender Jay DeMerit to injury and the man who replaced him - Argentine Martin Bonjour found himself at the centre of the decisive incident within minutes of coming on.
Donovan burst round the back of Bonjour into the area and the defender was ruled to have pulled back the U.S striker, although contact appeared minimal.
Donovan rose to convert the penalty and put the Galaxy into the next phase of the play-offs - a two-legged tie against the top-ranked team in the regular season, starting on Sunday in San Jose.
‘I’d watched Alisson since 2012, but he had no EU passport. I did my own work and thought if we were to spend money, he was the only one to spend it on’: Liverpool waited patiently for Brazilian goalkeeper before finally making £67m signing in 2018
'Winning the league at Old Trafford tops White Hart Lane – you can imagine Fergie saying, "Don’t let this mob beat us to win the title at our own stadium"': Arsenal legend preferred sealing 2002 title against Manchester United than in 2004 versus Spurs
