The striker’s first-half header clinched a second Premier League scalp for the Sky Bet Championship side after their victory at Wolves last month.
Henri Lansbury and Keinan Davis missed fine chances while Potters goalkeeper Adam Davies denied Ollie Watkins as Villa bowed out.
Villa boss Dean Smith made 11 changes from the team which beat Fulham 3-0 on Monday but last season’s runners-up were outfoxed by organised and disciplined Stoke.
With skipper Jack Grealish given a breather, Villa, who lost their 100 per cent start to the season, lacked inspiration and purpose in a meandering first half.
A tame header from Jacob Ramsey and Lansbury’s wayward effort were all the hosts could muster, although Stoke offered little until they took the lead after 26 minutes.
Michael O’Neill’s side had been compact and efficient before Jed Steer turned Nick Powell’s snap shot over.
It was the visitors’ first chance and they scored with their second, Vokes heading in the resulting corner from Jordan Thompson’s delivery.
Villa should have levelled four minutes later, though, only for Lansbury to plant a free header woefully wide from six yards.
Stoke have now kept six clean sheets in seven games this season but they profited from Villa’s wastefulness five minutes before the break.
Lansbury and Bertrand Traore were involved in finding Anwar El Ghazi to deliver an excellent low cross and a stretching Davis directed it wide at the far post.
Despite Villa’s chances Stoke had edged the contest since going ahead and almost doubled their lead eight minutes after the break.
Vokes had given Kortney Hause and Ahmed Elmohamady a difficult night and he escaped them again but could only direct Josh Tymon’s perfect delivery across goal.
Hause limped off soon after, being replaced by Ezri Konsa, but rather than upset their rhythm Villa began to click into gear.
El Ghazi cut in from the left and evaded several half-hearted challenges but his low drive was saved well by Davies.
Record signing Watkins was then thrown on with 20 minutes left and he immediately forced Davies to turn over his 20-yard effort.
Villa’s burst threatened to haul them level but they lost their momentum and, despite late pressure, resilient Stoke booked their spot in the last eight.
