Keane played a beautifully chipped ball into the path of Landon Donovan who rounded Quakes keeper Jon Busch for the opening goal at the StubHub Center in the 26th minute.
The Republic of Ireland international then made it 2-0 in the 43rd minute when he slipped it past Busch from the penalty spot despite the San Jose getting gloves on the ball.
Keane then netted his 12th goal of the season in the 67th minute with a well-struck half-volley from Sean Franklin's knockdown header.
The weekly award is Keane's second in three weeks following his hat-trick against Real Salt Lake in Week 25 on August 17.
2013 MLS Player of the Week
Week 27: Robbie Keane (LA Galaxy) Week 26: Kelyn Rowe (New England Revolution) Week 25: Robbie Keane (LA Galaxy) Week 24: Landon Donovan (LA Galaxy) Week 23: Lloyd Sam (New York Red Bulls) Week 22: Álvaro Saborío (Real Salt Lake) Week 21: Chris Rolfe (Chicago Fire) Week 20: Camilo (Vancouver Whitecaps) Week 19: Brad Knighton (Vancouver Whitecaps) Week 18: Alan Gordon (San Jose Earthquakes) Week 17: Camilo (Vancouver Whitecaps) Week 16: Kenny Miller (Vancouver Whitecaps) Week 15: Olmes García (Real Salt Lake) Week 14: Diego Fagundez (New England Revolution) Week 13: Marco Di Vaio (Montreal Impact) Week 12: Eddie Johnson (Seattle Sounders) Week 11: Will Bruin (Houston Dynamo) Week 10: Graham Zusi (Sporting Kansas City) Week 9: Tim Cahill (New York Red Bulls) Week 8: Jack McInerney (Philadelphia Union) Week 7: Brad Davis (Houston Dynamo) Week 6: Ryan Johnson (Portland Timbers) Week 5: Will Johnson (Portland Timbers) Week 4: Juan Agudelo (Chivas USA) Week 3: Bill Hamid (D.C. United) Week 2: Robert Earnshaw (Toronto FC) Week 1: Mike Magee (LA Galaxy)