Shaun Miller dedicated his moment of glory at Craven Cottage to his son, who was born last month.
The striker also admitted it was a timely confidence-boost to score his first goal in over 12 months having recently returned to action after a career-threatening knee injury, sustained on Boxing Day 2012.
Speaking in the media melee that ensued after he stooped to head home from Harry Maguire's knock down deep into extra-time, Miller said: "It was an unbelievable feeling to score so late in the game and that moment won't leave me for a very long time.
"I have found things a bit tough recently having returned after over 10 months on the sidelines, but this goal isn't for me it is for my little baby boy (Zac), who is only a few weeks old.
"To do it in front of our fans, who were tremendous on the night, was pleasing and for me I certainly hope it is the moment that will kick-start my season."
Miller felt the Blades deserved to beat Premiership opposition for a second time this year in this season's FA Cup, adding:
"We were comfortable for long periods in both normal and extra time and although many perhaps thought we were destined for penalties, we just had a sneaky feeling we could nick something on the break or from a set-piece.
"The goal came at a perfect time for us and was what we deserved for all the effort the lads put in during the previous 119 minutes.
"Fulham were shell shocked and simply didn't have time to mount a comeback."