Jon Walters wasted little time in atoning for his nightmare against Chelsea as he bagged an extra-time brace – at the right end this time – to ease Stoke past the plucky challenge of Crystal Palace.
The Ireland striker, who scored two own goals and missed a penalty on Saturday, delivered an ideal response, heading the Potters in front from close range five minutes into extra-time, and then sealing the deal with an emphatic finish 15 minutes later.
Cameron Jerome made it 4-1 late on as Stoke booked a fourth-round clash with Manchester City.
Kenwyne Jones had given Stoke the lead midway through the second half, with Glenn Murray levelling from the spot three minutes from time.
Sordell slid home a 64th-minute penalty and wrapped up victory nine minutes later as Bolton made sure of victory 10 days after blowing a two-goal lead in their Reebok Stadium clash.
The Black Cats dominated the first half, with Adam Johnson twice denied by superb saves.
After the break, though, Bolton seized the initiative. Sordell put them ahead from the spot after Jack Colback fouled Darren Pratley. They doubled their lead when Tyrone Mears squared for Sordell to force home his second.
El-Hadji Diouf's 76th-minute penalty proved decisive as Leeds came from behind to beat Birmingham 2-1 at St Andrew's.
Diouf, on his 32nd birthday, got the assist for Ross McCormack's the equaliser and then chipped his spot-kick down the middle to book a home clash with Tottenham.
Fulham needed a last-minute equaliser from Kieran Richardson to force extra-time with Blackpool, before Brede Hangeland snatched a 2-1 victory late on, and Jay Bothroyd gave QPR a 1-0 win at West Brom.