Arsenal were forced to come from behind against League Two Shrewsbury Town, while Manchester United cruised past Leeds.
Aston Villa crashed out to Bolton, Wolves thumped Millwall and Aldershot also progressed to the fourth round.
Arsenal suffered a scare after they were forced to come from 1-0 down against League Two Shrewsbury Town for a 3-1 win at Emirates Stadium.
The Gunners entered the clash stinging from a torrid start to their Premier League campaign, having suffered a 4-3 defeat at lowly Blackburn on Saturday.
Under-fire Arsene Wenger's troubles appeared to go from bad to worse when Shrewsbury ploughed ahead through James Collins in the 16th minute.
But the North Londoners hauled themselves level thanks to Kieran Gibbs before new-boy Alex Oxlade-Chamberlain capped his full debut with a goal in the 58th minute and Yossi Benayoun wrapped up the win.
Michael Owen, making his first appearance this season, was the star of the show for Manchester United as he inspired their 3-0 victory over fierce rivals Leeds United.
The 31-year-old proved he has not lost any of his firepower, trickling home an early opener for the Red Devils before doubling the lead in the 32nd minute.
Another veteran, Ryan Giggs, then added a sublime strike on the stroke of half-time to allow Sir Alex Ferguson's men to progress to the next round and uphold their unbeaten start to the season.
Stoke's clash with Tottenham went all the way to penalties, with the Potters emerging 7-6 winners after Spurs youngster Massimo Luongo saw his crucial spot-kick saved by Thomas Sorensen.
The match was locked at 0-0 at the end of both regular and extra-time and 18-year-old Luongo could not keep Spurs in it as he missed a sudden-death penalty at the Britannia Stadium.
Newcastle needed extra time to see off Nottingham Forest 4-3 in a dramatic encounter at the City Ground.
Peter Lovenkrands scored a double for the Magpies but goals from Robbie Findley and Matt Derbyshire saw Forest twice come from behind to leave things all square at the end of regular time.
Danny Simpson scored in extra time but his effort was cancelled out by Marcus Tudgay as the hosts kept the game alive.
The winner eventually came from Fabricio Coloccini late on in the extra minutes to dump the Championship side out of the competition.
Wolves may have suffered disappointing results in the Premier League of late but they had no trouble disposing of Championship opponents Millwall, romping to a 5-0 triumph at Molineux.
David Edwards opened the scoring for the hosts in just the third minute before further goals from Adam Hammill, George Elokobi, substitute James Spray and Adlene Guedioura sealed the rout.
Alex McLeish lost out on lifting the Carling Cup for a second consecutive year after Aston Villa were knocked out by Premier League rivals Bolton.
McLeish led his previous side Birmingham to cup success last season but any hopes of emulating that feat with Villa were banished when Chris Eagles and Gael Kakuta fired the Trotters to a 2-0 victory.
Blackburn held on for a 3-2 triumph over Leyton Orient, despite a late comeback from the League One strugglers.
Dean Cox pulled Orient back into contention with an 86th-minute strike but Rovers withstood their last-gasp assault.
Burnley enjoyed some relief from their poor start to the Championship season as they overcame League One high-fliers MK Dons 2-1.
Andre Amougou sealed the dramatic victory late on at Turf Moor to see the Clarets progress to the next round.
Crystal Palace gained revenge on Middlesbrough after suffering defeat to the same side in the Championship at the weekend, edging a 2-1 victory.
Wilfried Zaha and Calvin Andrew fired the Eagles to success at Selhurst Park.
Aldershot, the lowest ranked side left in the competition, booked their spot in the fourth round after disposing of Rochdale 2-1.
Danny Hylton hit home the winner after Michael Rankine cancelled out Ashley Grimes' opener just before the break.