Ched Evans and Richard Cresswell had the Blades 2-0 up early in the opening half, but the Iron fought back with two goals from Joe Garner ensuring the match was level at the break.
Lee Miller's first goal for the club early in the second-half was enough to seal a vital win for he Iron, who moved above the Blades in the table.
"My lads have just shown that they have got real guts, determination and the mental strength to hopefully see this through," said Baraclough.
“I’m made up for them. They are delighted because it was a horrible start. To find yourselves 2-0 down after seven minutes is not a very comfortable position to be in and they have gone and dug a result out, which didn’t seem likely.
“Seven points out of the last nine is something I don’t think people believed we could go and do.
“It will show the rest of the clubs around us that we aren’t happy being down there, we don’t think we should be down there come the end of the season and we are going to fight tooth and nail to stay in this division.”
The Blades boss Micky Adams felt his side should have defended better for all three goals they conceded.
"We had a good half an hour, dominated, got our rewards and were 2-0 up and cruising. Then we gave away a stupid penalty and all the old worries appeared," he said.
“The goals we conceded are criminal. three individual errors. We’ve talked about having a bit of desire in their box when we’ve got set-pieces and we lack that and we lack it when we’re defending as well, so you have to question the heart of the players.
"They certainly don’t want to get hurt, that’s for sure, defending them or attacking.