The enterprising playmaker soccered the ball over the line before touching down for the winner in the 75th minute to seal the three-match series 2-0 at Melbourne's Rectangular Stadium.
Playing at inside centre, Farrell also slotted five out of six shots at goal, with captain Dylan Hartley scoring the tourists' only other try in the first half of an enthralling and sometimes spite-filled encounter.
Australia were held scoreless for 35 minutes before Stephen Moore touched down in a rolling maul and were denied a second try time and again by brilliant English defence.
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(Reporting by Ian Ransom, editing by Pritha Sarkar)
