In the first minute however City could have taken the lead after Gareth Griffiths gave the ball away to Danny Allsopp in a dangerous position on the edge of the area and Neil Edwards did well to palm Allsopp's shot on to the bar and out for a corner.
But after 15 minutes, Rochdale began a period of pressure which saw them soak up possession and cause problems for City's defence, though they couldn't manage any shots on goal.
After 22 minutes Neil Redfearn shot well over from 30 yards, and shortly after Alton Thelwell badly mistimed a back header to keeper Boaz Myhill and the ball fell into the path of Grant Holt, who looked certain to score but Myhill deflected his shot on to the post and out of play.
In first half injury time, an 18-yard shot from Price was brilliantly kept out by an instinctive save from Edwards.
City made a crucial change in the second half, dropping Thelwell, who was not happy in central defence, for Stuart Green. They then missed a glorious chance to go ahead when Allsopp raced on to the ball down the right wing and crossed into Ben Burgess, who with the Dale defence nowhere, had all the time in the world to shoot, but he hit it straight at Edwards.
After 66 minutes Allsopp headed over before Delaney saw a shot saved as City began to find their feet a little, but Rochdale were still challenging for every ball and making things difficult for City.
Two minutes later, Leo Bertos shot just wide, and after 76 minutes he had another shot saved by the foot of Myhill as Rochdale began to dominate, buoyed up by an injury to Price which left City with 10 men as they had used all their substitutes.
But 10 minutes from time Delaney stunned the crowd with a superb individual goal which saw him hold up the ball for at least 35 yards before unleashing an unstoppable shot from 25 yards.