The talented winger built on his improving form and growing confidence with a fine individual goal that was enough to secure victory against such uninspired opposition.
Delivering on his promise to prioritise a competition which represents a realistic chance for his team to win a trophy, Palace manager Alan Pardew made only two changes to the team which last week lost 3-1 in the Premier League to Tottenham.
The first, forced upon him by Connor Wickham serving the first of his three-match suspension after he admitted an FA charge of violent conduct following an incident with Spurs' Jan Vertonghen, was a recall for Fraizer Campbell.
Lee Chung-yong also started over James McArthur in a more attacking-looking shape and, as Pardew perhaps predicted midweek when saying Palace's preparations for this fixture had been easier than Stoke's, their visitors made eight changes to the team that lost on penalties to Liverpool in Tuesday's Capital One Cup semi-final.
Only Erik Pieters, Philipp Wollscheid and Bojan were retained from the team that had then played over 120 minutes, and for all that they retained a strong look it often showed
Beyond occasional glimpses of quality from the talented Xherdan Shaqiri, Mark Hughes' team was largely flat and offered minimal threat, suiting Palace and particularly the in-form Zaha, whose recent run has brought him close to rediscovering the equilibrium lost with his failed transfer to Manchester United.
It was he who created, and scored, the game's opening goal in the 17th minute
Collecting possession in a central position on the edge of the area, he produced a classy moment of skill to beat Stephen Ireland and Marc Wilson and create the space to finish between goalkeeper Jakob Haugaard's legs.
Though Haugaard, making only his second appearance at Stoke, otherwise did little wrong, it is possible that at that point Hughes wondered if he had made a mistake in resting Jack Butland.
Their problems, however, were elsewhere, with their inability to create convincing goalscoring chances
Joselu headed over one reasonable Shaqiri cross towards the end of the first half, and Shaqiri also curled over on the stroke of half-time.
Palace did not quite share their problem
Theirs came largely in Campbell's lack of confidence in front of goal from chances new signing Emmanuel Adebayor, not even a substitute owing to a lack of match fitness, and reported Swansea transfer target Dwight Gayle, surprisingly also not involved, would have relished
In the 56th minute Campbell drew one fine save from Haugaard with a close-range, first-time shot following a cross from Pape Souare, but with another from Lee, despite time and space, he struck harmlessly over
Logically the one-goal lead and wasted chances would have made Palace appear vulnerable, but with Zaha so impressive and repeatedly creating chances, and Stoke offering so little, they rarely were and should have secured victory by a more convincing scoreline.
The addition of Adebayor to such promise might yet inspire a significant cup run
Source : PA