City started on the back foot and with only four minutes on the clock Phil Jagielka earned himself space on the edge of the box and fired a warning shot over the bar.
Jon Harley proved his worth throughout the match and had his first opportunity after 16 minutes when his 30-yard free-kick fizzed past everyone apart from Michael Duberry.
His poor touch almost conceded an own goal but he recovered well to defend against the arriving Alan Quinn.
Harley went closer after half an hour when he rattled the frame with a left-footed thunderbolt from 25 yards.
Stoke finally got a decent opportunity seconds before the break when a one-two with Kevin Harper gave Dave Brammer room to shoot from the left of the box, however his effort flew wide of Paddy Kenny's right post.
Tony Pulis' half-time team-talk seemed to work as the Potters exploded out of the box 11 minutes after the restart.
Noel-Williams cut inside from the left, beating Simon Francis, then striking a perfectly curled shot into Kenny's bottom right corner, leaving him no chance.
Only three minutes later Wayne Thomas' burst down the right flank and looping cross resulted in Noel-Williams' second of the afternoon.
Yet again, his accuracy was spot on as his cushioned header flew into the top left of the goalkeeper's net.
The Blades' loss of Danny Cadamarteri to injury meant the addition of new signing David Johnson, but a solid home defence denied then any clear chances.