The game began in positive fashion, with both teams playing high-tempo football in the early stages.
Just before the quarter-hour mark, Fulham striker Ross McCormack worked his way into the opposition area, but, under intense pressure from the Royals defence, the ex-Leeds United man fired over.
The home side had reason to celebrate just a few minutes later when a pinpoint Jordan Obita cross fell to Murray, whose towering header beat Cottagers goalkeeper Gabor Kiraly for the first goal of the match.
More drama ensued when visiting striker Matt Smith saw red in the 18th minute for a reckless challenge on Hope Akpan.
Nevertheless, Reading doubled their lead early in the second half, courtesy of another goal from Murray.
The 30-year-old was once again assisted by Obita, whose corner was headed in from very close range by the Crystal Palace loanee to put the home side two goals up.
Things would get even better for the Royals towards the end of the game as Simon Cox was able to release Nick Blackman, who went on to round Kiraly and fire home for his side's third goal of the afternoon.