Keane netted his first after 21 minutes, then bagged a second in the 34th and Mike Magee added a third five minutes later.
Steven Lenhart pulled one back eight minutes from the end but it was not enough for San Jose and the Galaxy held on for a 3-2 aggregate win.
They will next face either Real Salt Lake or the Seattle Sounders, whose first leg finished goalless.
The Houston Dynamo held on to claim their spot in the Soccer Eastern Conference final, but they will have to wait to find out their opponents as more bad weather on the east coast meant the New York Red Bulls and DC United saw their match postponed.
The Dynamo were grateful for their two-goal first-leg advantage as Sporting Kansas City beat them 1-0 in the return fixture.
Seth Sinovic scored the only goal after 64 minutes in KC but Sporting could not find another goal and Houston won 2-1 on aggregate.
With the Red Bulls and United level at 1-1 from their first leg, the second game was postponed for 24 hours because of a blizzard in New Jersey.