Agyemang kept a cool head to finish with aplomb after impressive performances by new boys Lee Hendrie and Ricardo Fuller had inspired City to produce a much-improved display.
The signing of Hendrie, on loan from Aston Villa, had persuaded a group of disenchanted Stoke fans to abandon their plan to dish out 10,000 red cards in protest against manager Tony Pulis.
But there was still an uneasy atmosphere among the home support as Preston made a confident start with David Nugent threatening with an early header from Graham Alexander's free-kick.
Stoke gradually began to find their feet however and Hendrie and Fuller were to the fore as the Preston goal game under strong pressure.
Hendrie had an eight-yard volley blocked on the line from Peter Sweeney's 15th minute corner, and then the former England midfielder struck the bar with a 20-yard free-kick.
And it was no more than Stoke deserved when Fuller opened the scoring against one of his former clubs four minutes before the interval.
Sweeney made the telling pass and Fuller took advantage of a lack of concentration in the visitors defence to race clear and place a low shot past Carlo Nash.
Fuller had a chance to add a second in the 55th minute, but this time skewed his shot horribly off target after hunting down Michael Duberry's punt upfield.
Stoke continued to boss most of the play and Preston manager Paul Simpson had seen enough by the 63rd minute when he introduced Danny Dichio to beef up his ineffective forward line.
And the visitors were level within seconds as the home defence, which had been rock solid until then, switched off completely.A long ball from Chris Sedgwick found Agyemang in acres of space and he sprinted away and beat Steve Simonsen with a confident chip.
Fuller's last piece of the action before limping off with a strained hamstring was a clever pass which invited Hendrie to restore Stoke's lead.
But the debutant, who was tiring badly by this stage, dallied over his shot for too long and an excellent chance had gone.