Goals from Keiron Durkan and Alun Armstrong enabled the Second Division side to add to their victims in the Coca-Cola Cup, where they have a home tie with Southampton to look forward to on Tuesday.
County took the lead in the 25th minute. Luis Cavaco skated past Justin Whittle and his low cross was despatched as Durkan stole in unmarked.
Dave Jones' side then withstood an onslaught in the second half before rubbing salt in the wounds of Stoke's manager Lou Macari when they broke out for Armstrong to slide in the second goal in injury time.
At Filbert Street, Leicester saw off the First Division strugglers, Southend United, 2-0. Steve Claridge eased his side's nerves with his eighth goal of the season in the 40th minute after Ian Marshall had headed a centre from the Swede, Pontus Kamark, into his path.
Marshall himself added the second three minutes after half-time, his third goal since his pounds 800,000 move from Ipswich. Garry Parker threaded the ball into his path and Marshall planted a low drive past Simon Royce from 10 yards out.
Leicester now meet Norwich in the fourth round, but it was not hard to see why Martin O'Neill is looking to strengthen a squad decimated by suspensions and injuries. He is understood to have had a pounds 1m bid rejected for the Port Vale pair of winger Steve Guppy and midfielder Jon McCarthy.
Referee Gerald Ashby provoked uproar when he called off Coventry's tie against Woking less than an hour before kick-off. Ashby ruled the Highfield Road pitch unplayable, to the astonishment of both clubs.
"I can't believe what he has just done," Woking's chairman, Phil Ledger, said. "This pitch is perfectly playable in my opinion and all I can do is apologise to all our supporters who have battled up here through the freezing fog."
Coventry's chairman Bryan Richardson, whose club will now make a third attempt to play the game on 25 January, said: "I cannot believe it. I wouldn't have thought this pitch was anything but playable."
Ashby himself said: "I don't believe semi-professional and professional footballers can perform in conditions like these." But Clive Walker, Woking's former Chelsea winger, said: "We would love to have played on this ground. It's not half as bad as some pitches we've played on this season.
A headed goal 13 minutes from time by Paul Gascoigne earned Rangers a 1-1 at Kilmarnock last night after Colin McKee had put the home side ahead a minute into the second half. Rangers' lead over Celtic at the top of Scotland's Premier Division is now nine points.Reuse content