Walker's bizarre backheel in his own box was intercepted with ease and made its way to Jayden Bogle, who lashed one past Ederson to score a late equaliser.
The full-back, who grew up a Blades fan, was furious with himself, kicking an advertising board in frustration.
With just minutes left on the clock, Bramall Lane was sent into a frenzy as they believed they had taken a crucial point off the Premier League champions.
However, there was a cruel twist to the tale as moments later, Rodri's bullet into the top corner restored City's lead.
Walker's blushes appear to have been spared by the Spaniard while Erling Haaland made up for his missed penalty by scoring the opener after 60 minutes.
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It might not have been a vintage display from City but they have secured three big points to remain the only side with a perfect start.
They returned to the top of the table with three wins out of three after earlier victories over Burnley and Newcastle.
But it did not come easy after a tough first-half display from the treble winners.
Haaland had the chance to score from the penalty spot after John Egan was adjudged to have handled in the box.
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However, despite scoring his last seven efforts from the spot, the 23-year-old smashed his penalty against the post.
But the Norway international had the last laugh when he nodded in a clipped cross from Jack Grealish to give City the lead.
The striker hardly celebrated as he looked more relieved than anything.
And despite dominating, City could not kill the game off before Walker's horror error gifted the Blades an equaliser on 85 minutes.
But United hearts would break after they believed they had netted a late equaliser when Rodri popped up.
Phil Foden tried to control a ball but, perhaps fortunately, it fell to Rodri, who was just behind him.
And the Spaniard thrashed the ball into the top corner that left Wes Foderingham statuesque just three minutes after Bogle's strike.