Geovanni levelled the score, then with nine minutes remaining, substitute Craig Fagan squared the ball for fellow substitute Caleb Folan to slot the ball home.
Tigers boss Phil Brown was delighted with the result and the impact of his substitutes.
"The spirit of the football club was there for everybody to see."
"The fitness levels in the second half were incredible, as was the passion and the drive. The character was tremendous.
"Before the game we said to the players that Fulham didn't travel too well last season, and we tried to exploit their weaknesses.
"We stuck to a game plan and the substitutions changed the game late on.
"Could I have asked for more? I would have liked a clean sheet as those are going to be very important this season."