City looked the most comfortable team with Michael Ricketts having his seventh minute shot deflected over by a last-ditch Martin McIntosh challenge.
However the Millers were in no way pinned down and broke forward five minutes later with Michael Keane leading the charge.
His pass inside allowed Paul McLaren a sight on goal and his 25-yard drive was turned for a corner by Steve Simonsen.
The visitors took the lead in the 23rd minute when a mis-hit cross deflected off Michael Duberry and fell to John Mullin on the right of the box.
His chipped cross found Martin Butler who headed firmly past Simonsen.
The Potters did manage to create an opening before the break but sadly for Tony Pulis it didn't produce an equaliser.
After a game of head tennis between Clive Clarke and Wayne Thomas the ball finally fell to Kevin Harper on the right of the area but his volley flew inches wide.
The addition of Carl Asaba and Lewis Neal after the interval seemed to help a struggling City side but the much-needed goal still proved elusive.
Neal should have done better in the 56th minute when Harper did well to cross from the right byline but the substitute's weak header was easily pushed around the post by Mike Pollitt.
The goal finally arrived for Stoke with seven minutes left when a long cross from the left was met with a looping header from Gifton Noel-Williams.
The towering striker beat McIntosh in the air and sent the ball into Pollitt's top right-hand corner from 12 yards.
However, their hopes were quashed when hero Noel-Williams turned villain after McLaren's parried shot bounced off his thigh and into his own net.