Katie Wilkinson had put the Blades ahead just eight minutes into the game and despite having much the better of the first half, the hosts pegged them back through Vyan Sampson’s goal in the second half.
But Fergusson popped up on 75 minutes to pinch the win.
Beaming Blades boss Carla Ward said: "These girls will not roll over - they do not want to get beat and when that equaliser went in, the attitude and desire within them was exceptional.
“The attitude is unbelievable, and I love working with them.
"They're enjoyable to watch, enjoyable to work with, they drive each other every day and right now we've got something special, this is a special team.”
United started on the front foot and the first chance came for Wilkinson, who volleyed straight at home stopper Lucy Thomas.
Less than a minute later though and Carla Ward’s side led.
A cross from Fergusson was spilled by Thomas under pressure from her own defender and Wilkinson was gifted the opener from close range.
London City came out firing after the break and they equalised from a corner when Sampson prodded home from the edge of the six-yard box.
United found themselves under pressure for the next 10 minutes but they won it in style with 15 to go when Fergusson ran forward from the halfway line and curled a superb effort into the far corner.
London put the pressure on as the clock ticked down, but the Blades held on.
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