In the all-Premier League tie at Villa Park, a brace from Jermain Defoe, plus further goals from Paulinho and Nacer Chadli helped the four-time winners of the competition through in style.
Andre Villas-Boas' side dominated the opening 45 minutes and they made their pressure pay on the stroke of half-time following a wonderful flowing move.
Lewis Holtby's delightful chip into the area was flicked home by goal poacher Defoe.
They doubled their lead just four minutes into the second period as an outswinging corner from the left struck Matt Lowton before ricocheting off Paulinho and past the helpless Villa goalkeeper Jed Steer at his near post.
With four minutes remaining, a mistake by Yacouba Sylla allowed Defoe to pick out Belgium winger Chadli in space and he calmly added a third.
They completed the rout when another Sylla error gifted Defoe his second of the night and his sixth goal in only his third start for the club this season.
The visitors made light of having to play twice in three days with their eighth victory in nine games.
But the outcome hinged on a bizarre incident immediately after the restart, which Villa boss Paul Lambert was convinced should have reduced Tottenham to 10 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 as he kept a clean sheet.