A first-half penalty to Andy Johnson and second-half strikes from substitute Eddie Johnson and Norwegian Erik Nevland helped the Cottagers make amends for their surprise 2-1 loss to A-League newcomers Gold Coast United in Queensland last Wednesday.
Johnson ran on to a superb Danny Murphy through pass but was bundled to the ground by Melbourne skipper and former Rangers and Millwall defender Kevin Muscat and was awarded a penalty.
Johnson took the kick and neatly dispatched it low to the keepers left in the 32nd minute.
Fulham, who have qualified for the inaugural Europa League this season after finishing seventh in the English Premier League last season, were far more enterprising in the second half.
They made the match safe in the 67th minute when American Eddie Johnson raced on to a ball and slotted home past goalkeeper Glen Moss for 2-0.
South Korean Seol Ki-Hyeon dispossessed Victory midfielder Billy Celeski in the middle of the pitch and flicked a perfect pass into the path of Nevland who clinically made it three on 73 minutes.
Nevland had an opportunity for a fourth goal when he attempted to lob the goalkeeper with a delicate half volley, only for it to rebound off the crossbar.
Fulham manager Roy Hodgson, who played his strongest possible line-up from kick-off, said that made a huge difference to the result compared with the surprise loss to Gold Coast where he experimented.
“It was a better performance, but tonight we played with what we considered our best line-up for 60 minutes,” Hodgson said.
“Melbourne were good, they were very competitive, created some good chances in the first half.”
Fulham’s Australian goalkeeper Mark Schwarzer was substituted with 25 minutes remaining to generous applause from the crowd of 20,000.
With one win and one loss so far in Australia, Fulham round off their three-match tour with another friendly against Perth Glory in Perth on Wednesday.