The 20-year-old, who looks certain to be in the top-flight next term amid links with Leeds, Newcastle and Brentford, scored the second goal of the match to give Steve Cooper's side a real advantage following Jack Colback's opener inside the first 10 minutes.
The Blades had chances of their own and were the dominant side early on in both halves, and got their reward with an injury goal from Jack Robinson to keep the tie alive going into Tuesday's second leg at the City Ground.
It was a lively start to the match as Ryan Yates played a wonderful ball to Forest star Johnson who forced an awkward clearance from Chris Basham inside four minutes.
While the Blades settled into the game, the opener came just five minutes later as Sam Surridge squeezed a cross into the penalty area which Colback converted after an unfortunate slip from Ben Osborne.
Forest smelled blood as they continued to flood forward with Surridge, Philip Zinckernagel and Johnson all having opportunities to double their lead inside the first quarter of the match.
Both sides pushed forward in what was a truly entertaining first half at Bramall Lane, however it was Forest who peppered the Sheffield United goal in the last 10 minutes of the half, forcing Wes Foderingham into a spectacular double save late in the half.
Going into the break, talkSPORT co-commentator, Chris Iwelumo, baffled as to how Cooper's side weren't further ahead at the break.
He said: "Nottinham Forest could have had two or three more goals. They had massive chances.
"There's a lot of football to be played, but Steve Cooper has to keep them going."
While the Blades certainly weren't outclassed in the first half, they managed to up their game in the second period they caused problems for Forest with five efforts in the first 15 minutes of the half.
However Forest managed to double their lead about 70 minutes when Joe Lolley laid it back to Johnson who slammed the ball into the top corner of the net to make it 2-0.
That effort really took the wind out of the home side, however they managed to get a late consolation in the shape of a Robinson header that ensured that the Blades are well and truly in the mix going into the return leg at the City Ground on Tuesday night.