The score remained at 1-1 until extra time when the Gunners scored three more times, twice from the penalty spot, to progress 4-1.
Henri Lansbury had put Arsenal deservedly ahead in the first half only for Robbie Keane to level early in the second half as Spurs began to fightback.
The clubs tied at a 1-1 stalemate in regular time but the hosts dominated on spot-kicks 4-3 to deservedly progress.
The Bees then missed a penalty in normal time but made no mistake when it came to sudden death from 12 yards.
Owen Coyle's Bolton suffered a shock defeat on his return to Burnley were he endured a torrid time from the home support on his return.
Wade Elliott scored the only goal of the game on the stroke of half time.
West Ham triumphed at Sunderland in the all Premiership clash.
Frederic Piquionne put the Hammers ahead in the first half but Asamoah Gyan restored parity almost immediately.
New signing Victor Obinna got the eventual winner to bring a little cheer into the Hammers miserable start to the season.
Another all Premiership clash ended in a 2-0 win for Stoke over Fulham at the Britannia Stadium.
Danny Higginbotham in the first half and Kenwyne Jones late on did the damage.
Aaron Wilbraham scored a late consolation for the League One visitor’s.
Lee Hughes actually gave County the lead before Nenad Milijas levelled from the penalty spot with seven minutes remaining.
Steven Fletcher and a Kevin Doyle brace in extra time gave Wolves a hard fought win after Kevin Smith had reduced the arrears.