Sturrock said: "Carl has played at the highest level - for club and country - and his experience shone through today.
"He scored a great goal but his leadership qualities were there for all to see.
"He made a big difference to us and he kept everyone going, and that is what you need when you are in our position.
"We carried on from where we left off in the second half against Palace on Tuesday and battled throughout today.
"I have not lost the dressing room and that showed again today. We are all in this together and it's just a shame that we gave away two zany goals, otherwise I would be here celebrating a victory."
Fletcher angled home his strike after left-back Gary Sawyer headed Paul Gallagher's right wing corner back across the face of goal.
Blades striker Danny Webber - who steered the ball just wide in the first half - pounced on a scuffed Romain Larrieu goal-kick to race 35 yards and beat the home goalkeeper with a clinical finish in the 63rd minute.
But Sturrock's spirited Argyle side bounced back in style and went 2-1 ahead on 70 minutes when Sawyer's throw-in was headed down to Gallagher by Rory Fallon.
Argyle's top scorer Gallagher - on loan from Blackburn - superbly steered the ball into the far corner with a sweeping shot which took his goal haul to eight.
United were not finished and makeshift striker Greg Halford headed his third goal in four games when he stooped to power home Gary Naysmith's deep cross from the right.
Blades boss Kevin Blackwell - a former Argyle coach and goalkeeper - said: "I thought we settled well and had the better of the first half.
"I know through being here how tough it is to get anything at Plymouth and the home crowd played their part today.
"With the position that Plymouth find themselves in, I knew it would be tougher than ever and I am delighted with the way my players have come away with something.
"They have come back twice and could have gone on to win it in the end.
"We are low on numbers and yet you wouldn't have guessed that by looking how well the players did out there today."