Houston Dynamo, meanwhile, held on to book a place in the Eastern Conference final with a 1-0 defeat to Sporting Kansas City still enough to give them a 2-1 aggregate victory.
Trailing 1-0 from the first leg, defending champions Galaxy looked determined from the outset with David Beckham going close with two free-kicks inside the opening 10 minutes.
San Jose suffered a setback when central defender Victor Bernardez had to be substituted with injury, forcing a reshuffle at the back.
Keane brought Galaxy level on aggregate with a fine solo goal in the 21st minute, running at the San Jose defense before driving the ball in off the inside of the post with a well-struck effort from outside the area.
The Irishman struck again when he made a perfectly timed run and was found by a delightfully weighted pass from Landon Donovan, before rounding Earthquakes keeper Jon Busch and slotting home.
Donovan was the creator again when he picked out Mike Magee, who fired in a first-time shot to make it 3-0 with six minutes left in the first half.
San Jose substitute Alan Gordon pulled one back in the 82nd minute but the Galaxy held firm to eliminate the team which had won the 'Supporters' Shield' for top regular season record.
The Galaxy will face the winner of Thursday's game between Real Salt Lake and the Seattle Sounders.
Houston, beaten finalists in last year's MLS final, will play the winners of the other Eastern Conference semi-final between New York Red Bulls and DC United, which was postponed to Thursday because of snow in the New Jersey area.
Dynamo, two-times MLS Cup winners under their coach Dominic Kinnear, took a two goal lead to Kansas City and had their backs to the wall for most of the game.
Sporting enjoyed 75 percent possession in the first half but did not manage a breakthrough until a diving header in the 64th minute by Seth Sinovic from a deep Graham Zusi cross.
That prompted some frantic attacks from Kansas City but they were unable to get the second goal which would have sent the match into extra-time.
The defeat was a bitter blow for Sporting who had finished the regular season five points clear at the top of the Eastern Conference but went out to the same team who eliminated them last season.
There was disappointment of a different kind for DC United fans who had travelled to New Jersey for the clash with the Red Bulls but were left without a game.
After 45 minutes of attempting to clear the field of snow, officials decided to postpone the game until Thursday to the frustration of DC head coach Ben Olsen.
"Have you seen the field? It looks fine to me," Olsen was quoted as saying by the MLS website.
"I'm baffled that we can't play this game. It's a playable field from my end. Maybe I'm wrong.
"I'm upset because I've got some guys that, by the look in their eyes, they were ready to go today," he added.
But Red Bulls' Swedish coach Hans Backe took a different view.
"In my opinion, this was a very easy decision to postpone a game. You can't see the lines, it's not football playing on these conditions, a risk for the health of the players.
"You can't do it because this pitch is not heated. If it was a heated one, then probably you could have done it."
The tie stands at 1-1 after the first leg.