The head coach admitted to “having sleepless nights” about switching from his normal 4-4-2 formation to match the Blades’ wing-back system after a run of three successive wins.
But it snuffed out the free-scoring visitors to such an extent that Niki Maenpaa did not have a testing save to make at Ashton Gate - and an 81st minute header from substitute Marley Watkins bagged another three points.
Johnson said: “It doesn’t matter what game plan you employ if the players do not carry it out - and today they did it to perfection.
“Switching things around was not a decision I took lightly, but I felt it was right to set up to match Sheffield United because of their quality.
“They create very good overloads down both channels so we had to work on nullifying that and going toe-to-toe athletically with each individual opponent.
“The key point to recognise is that they have been getting off more shots, putting in more crosses and passes into the box than any team in the Championship.
“We have talked about getting a depth in defensive areas and we are starting to get that. It was a big performance and a big win for us.
“I didn’t envisage the game being as boring as it was for 55 minutes, but our substitutes turned the game on its head. We are a fit team anyway, but we brought fresh legs on and it made a difference.”
United boss Chris Wilder was not sure Watkins was aiming for goal when his glancing header from a right-wing cross by fellow substitute Callum O’Dowda sneaked in at the far post.
But he admitted it was a fine goal from City’s perspective, even though it left his side with nothing to show for a committed and positive display.
Wilder said: “It’s the worst feeling in the world when you play well and lose, as we did today. But we failed to make the most of the periods when we were on top.
“We should have come in at half-time, not one, but probably two up. Any manager will tell you that the first goal in Championship games is so important and we should have got it.
“That would have meant them having to chase the game. Instead, it was the other way around and we were not as careful in possession trying to get back into the match after they had scored.
“It was a very good away performance without the most important bit, which is winning the game.
“They paid us the compliment of changing their system around, while on a decent run in a very competitive division.
“If you don’t play well and lose or the other side do so well you can’t lay a glove on them, you accept it. Today we have played well enough to win, but have not done enough in the opposition box.”
David McGoldrick missed the best United chances in the first half, while City’s best period came in the final 20 minutes when they might have netted more than once.
A fourth successive win for Johnson’s men lifted them to third in the table.