The visitors made light of having to play twice in three days as Jermain Defoe and Paulinho struck either side of half-time before Nacer Chadli blasted in and Defoe tucked home his sixth of the season to give them a deserved win, matching their easy league win on the same ground last term.
But the outcome hinged on a bizarre incident immediately after the restart, which Villa boss Paul Lambert was convinced should have left Tottenham reduced to ten men.
Introduced for Libor Kozak at the interval, Nicklas Helenius got round the back of Jan Vertonghen as they chased Matt Lowton’s forward pass into the box. In his desperation to recover the lost ground, Vertonghen stumbled and as he was falling made a grab for Helenius. The Belgian succeeded only in grabbing the striker’s shorts, yanking them down to his knees just as he was about to shoot.
Helenius carried on anyway, blasting over from an acute angle. To Lambert’s disbelief, referee Jon Moss opted to give a goal-kick rather than a penalty that surely would have been accompanied by Vertonghen’s exit.
That Paulinho’s goal came within two minutes of such a strange incident underlined it was not going to be Villa’s night as Spurs’ successful start to the season continued.
It also made it a successful night for their veteran former Villa keeper Brad Friedel.
Manchester City continued where they left off in Sunday’s 4-1 drubbing of Manchester United by putting Wigan to the sword.
Stevan Jovetic claimed his first two goals in sky blue as Manuel Pellegrini’s side eased into the fourth round.
Edin Dzeko and substitutes Yaya Toure and Jesus Navas were also on target as City completed a routine 5-0 win over the Championship side at the Etihad Stadium.
City made ten changes from the side which thrashed rivals Manchester United in Sunday’s derby at the same venue but there was no let-up in the intensity of their performance.
Former Celtic striker Gary Hooper was on target six minutes from the end of extra time as Norwich overcame Watford 3-2 at Vicarage Road.
Hooper had earlier hit the injury-time equaliser and Josh Murphy also scored as Norwich fought back from a 2-0 deficit built on strikes by Marco Faraoni and Javier Acuna.
Hooper calmly slotted the winning goal of the game as he coolly finished when through on goal with just minutes of extra-time remaining.
Fulham fought back from 1-0 down to overcome Everton 2-1 with Darren Bent hitting a 69th-minute winner after Dimitar Berbatov had cancelled out Steven Naismith’s opener.
Sunderland made a positive start to life without sacked manager Paolo Di Canio by dispatching Peterborough 2-0 with strikes from Emanuele Giaccherini and Valentin Roberge.
Cardiff staged their own fightback after trailing 2-0 to West Ham, only for Sam Allardyce’s side to finish 3-2 winners through a late header by the former Hibs striker Ricardo Vaz Te.
Ravel Morrison and Matthew Jarvis fired the Hammers ahead and Cardiff responded through Craig Noone and Peter Odemwingie, only to have their hearts broken by Vaz Te.
Fernando Torres and Ramires scored in six first-half minutes as Chelsea swatted aside Swindon 2-0 at the County Ground.
Danny Ings nodded in Burnley’s winner in a 2-1 home victory over Nottingham Forest having already hauled his side back into contention with the equaliser of Matt Derbyshire’s opener.
There were few fireworks at the KC Stadium where Hull’s Nick Proschwitz produced the only goal against Huddersfield and he should have had a second.
Derby slumped to their first away defeat of the season, losing 2-1 to Leicester City despite taking the lead through Chris Martin.
Anthony Knockaert and Danny Drinkwater were on target to ensure Leicester progressed into the last 16.
Gaston Ramirez and Jos Hooiveld ensured Southampton progressed in a 2-0 victory over Bristol City, but Saints were made to work for their place in the next round.