The majority of the chances had gone the way of the visitors, but a fine cross from Morgan Gibbs-White was nodded expertly home into the net of the side who had seen a Brennan Johnson penalty saved by Wes Foderingham earlier in the game.
However, an in-swinging corner from James Garner with just 30 seconds left on the clock was headed home by Yates to salvage a point on the road for Steve Coopers men.
Both sides came into the game on the cusp of the play-off places, with United just one singular point away from the top six and their visitors three away.
Nottingham Forest named just one change to the side that defeated Bristol City 2-0 at the City Ground last weekend, with Jack Colback taking the place of the ineligible Sheffield United loanee Max Lowe on the left of the defence. Ryan Yates came into the midfield in his place.
• Story of the match
Forest got onto the front foot almost immediately, with Brennan Johnson breaking into room on the edge of the box to force a save from Wes Foderingham inside the first minute.
From the resulting corner, Keinan Davis rose highest to barely loop a header over the bar in a bright opening period for The Reds.
Philip Zinckernagel found himself in behind after a great ball in from Keinan Davis, but his effort one-on-one was thwarted by Foderingham.
After an earlier shirt-pulling infringement went unheeded, Forest were awarded a penalty in the 32nd minute as Djed Spence went down in a tangle of legs with Rhys Norrington-Davis.
Brennan Johnson smashed his penalty down the middle, but it wasn’t enough to get past Foderingham who beat it away for the second consecutive home game.
Cook was involved again at the other end five minutes later, as the experienced defender slid in expertly to deny Gibbs-White a chance at goal.
For all of Forest’s chances and pressure, it was United who grabbed the lead in the 69th minute, as Billy Sharp headed home an exceptional cross from Gibbs-White to give his side the lead against the run of play.
Forest continued to carve out opportunities, however, as some fine play on the edge saw Zinckernagel find room in on the left of the box, but his left-footed strike smashed the side netting.
A hat-trick of chances fell sharply to The Blades two minutes later, as Ethan Horvath showed some fantastic reflexes to beat away a header and a follow-up shot from Davies following a corner.
Forest’s track record of late goals continued to the relief of the travelling fans, as a final corner was nodded over Foderingham by Ryan Yates to rescue a point for The Reds at the death.
The result see’s Sheffield United’s chance to get into the top six cruelly ripped away, with both sides holding place in the table.