Viduka has now scored a priceless 11 goals in seven Premiership matches, taking his tally for the season in all competitions to 19.
He needed just four minutes to calm Leeds' nerves with the opening goal.
Gary Kelly hoisted a corner into the goalmouth from the right and Viduka enjoyed a free header, to leave Fulham's interim manager Chris Coleman asking questions of his defenders.
Viduka owed his second goal, three minutes after the break, to the Australian connection.
Harry Kewell pounced on Sylvain Legwinski's back pass, nipped between Jon Harley and Zat Knight before seeing his shot blocked by keeper Maik Taylor.
However, the rebound fell kindly for Viduka to lash a 12-yard shot inside the right-hand post.
Leeds began the match in 17th place - their lowest position for six-and-a-half years, but Peter Reid kept the side that lost disappointingly at Southampton four days earlier.
Fulham, looking to build on their 2-1 victory over Newcastle, had striker Elvis Hammond making his first start, but the youngster was too often left to battle on his own as the Cottagers packed their midfield.
Just six minutes after Viduka's goal, Fulham suffered another blow when Martin Djetou limped off, to be replaced by Knight.
One of the highlights of a dull encounter was a storming 70-yard gallop by Leeds defender Michael Duberry, but Fulham had cause to complain on two counts.
Duberry clearly handled to get the ball under control before his storming run. Then, to add insult to injury, he hurled himself to the floor between two defenders to win a dubious free-kick.
Alan Smith and Kewell went close to increasing Leeds' advantage with low shots, but Fulham's lack of adventure left home keeper Paul Robinson a spectator.
Fulham were a big disappointment and although Leeds were below their best they were worthy winners of a match that will quickly be forgotten.