Match ends, Tottenham Hotspur 2(4), Watford 2(2).
Tottenham midfielder Dele Alli will remember his Milton Keynes homecoming "for all of his life", says manager Mauricio Pochettino.
Alli, who began his career at MK Dons, scored the winning penalty in a shootout as Tottenham beat Watford to reach the Carabao Cup fourth round.
The game was played at Stadium:MK as work continues on Spurs' new stadium.
Isaac Success put Watford ahead, goals from Alli and Erik Lamela made it 2-1 before Etienne Capoue equalised.
Success and Will Hughes scored for the Hornets in the shootout but Spurs goalkeeper Paulo Gazzaniga denied Capoue and Domingos Quina.
Son Heung-min, Lamela and Fernando Llorente converted Tottenham's opening three penalties before Alli - captain for the match - scored.
"I gave him the armband because it was so exciting for him to play here in his home town," said Pochettino.
"It is difficult for him to have another possibility to play here again and I wanted to provide him a very good feeling. I hope he appreciates a lot my gesture.
"He was inspired by the occasion. To play here he was so excited. The energy in the previous day was amazing."
England international Alli played 76 games for MK Dons, scoring 20 times, before joining Tottenham for £5m in 2015.
"We can feel here the love that the people feel for him and that was fantastic for us," added Pochettino.
"For him it is an experience he will remember for all of his life. To be Tottenham captain and score is a fantastic night for him."
Tottenham expected to move into the 62,000-seater ground by 15 September, but the work has overrun, with no known date for its completion.
They played their first two home Premier League games of the season at Wembley, but that was unavailable for this tie after staging Saturday's world heavyweight title boxing match between Anthony Joshua and Alexander Povetkin.
That meant the four-time League Cup winners played a 'home' match more than 50 miles away from their new stadium, in front of a crowd of 23,650.
"I want to say thank you to our fans," said Pochettino.
"They need to be praised by myself on behalf of the players, the staff to come here and offer their support. They made a massive effort.
"Thank you to all the town of Milton Keynes and all the club - they welcomed us in a very good way. They helped us in every way."
The fans had to endure a poor first half with neither side having a shot on goal in the opening 20 minutes.
But 40 seconds after the interval Success ran through the middle of the Tottenham defence, held off a challenge from Serge Aurier and shot past Gazzaniga.
Tottenham went down to 10 men when Aurier had to leave the field injured after Pochettino had made his three substitutions.
However, substitute Christian Kabasele was dismissed only four minutes after coming on when he pulled down Alli for the equalising penalty.
Lamela put Spurs ahead with four minutes remaining with a calm finish from Mousa Dembele's through ball.
However, Capoue equalised against his former side when his shot deflected off Ben Davies.
Tottenham rested Harry Kane and Christian Eriksen, while Watford made 10 changes from their last Premier League match.
Watford manager Javi Gracia said: "We played really well but there were some decisions that were hard to accept.
"What I saw was Dele Alli and Christian Kabasele fighting for the ball and they both went to the ground.
"The penalty is one thing but I cannot understand the red card. With every game we play I'm more proud of my players, they have performed very well."
Spurs, who are fifth in the Premier League, travel to Huddersfield on Saturday at 15:00 BST, when fourth-placed Watford face Arsenal at Emirates Stadium.
Match ends, Tottenham Hotspur 2(4), Watford 2(2).
Penalty Shootout ends, Tottenham Hotspur 2(4), Watford 2(2).
Goal! Tottenham Hotspur 2(4), Watford 2(2). Dele Alli (Tottenham Hotspur) converts the penalty with a right footed shot to the bottom left corner.
Penalty saved! Domingos Quina (Watford) fails to capitalise on this great opportunity, right footed shot saved in the bottom left corner.
Goal! Tottenham Hotspur 2(3), Watford 2(2). Fernando Llorente (Tottenham Hotspur) converts the penalty with a right footed shot to the top left corner.
Goal! Tottenham Hotspur 2(2), Watford 2(2). Will Hughes (Watford) converts the penalty with a left footed shot to the bottom left corner.
Goal! Tottenham Hotspur 2(2), Watford 2(1). Erik Lamela (Tottenham Hotspur) converts the penalty with a right footed shot to the centre of the goal.
Penalty saved! Etienne Capoue (Watford) fails to capitalise on this great opportunity, right footed shot saved in the bottom left corner.
Goal! Tottenham Hotspur 2(1), Watford 2(1). Son Heung-Min (Tottenham Hotspur) converts the penalty with a right footed shot to the centre of the goal.
Goal! Tottenham Hotspur 2, Watford 2(1). Isaac Success (Watford) converts the penalty with a right footed shot to the top left corner.
Penalty Shootout begins Tottenham Hotspur 2, Watford 2.
Second Half ends, Tottenham Hotspur 2, Watford 2.
Foul by Son Heung-Min (Tottenham Hotspur).
Will Hughes (Watford) wins a free kick on the left wing.
Goal! Tottenham Hotspur 2, Watford 2. Etienne Capoue (Watford) right footed shot from outside the box to the high centre of the goal. Assisted by Adrian Mariappa.
Corner, Watford. Conceded by Davinson Sánchez.
Corner, Watford. Conceded by Davinson Sánchez.
Goal! Tottenham Hotspur 2, Watford 1. Erik Lamela (Tottenham Hotspur) left footed shot from the centre of the box to the bottom right corner. Assisted by Mousa Dembélé.
Foul by Ben Davies (Tottenham Hotspur).
Isaac Success (Watford) wins a free kick in the attacking half.
Attempt missed. Fernando Llorente (Tottenham Hotspur) left footed shot from outside the box is high and wide to the left.
Harry Winks (Tottenham Hotspur) wins a free kick in the attacking half.
Foul by Domingos Quina (Watford).
Substitution, Watford. Etienne Capoue replaces Ken Sema.
Goal! Tottenham Hotspur 1, Watford 1. Dele Alli (Tottenham Hotspur) converts the penalty with a right footed shot to the bottom left corner.
Christian Kabasele (Watford) is shown the red card.
Penalty Tottenham Hotspur. Dele Alli draws a foul in the penalty area.
Penalty conceded by Christian Kabasele (Watford) after a foul in the penalty area.
Harry Winks (Tottenham Hotspur) wins a free kick on the right wing.
Foul by Adam Masina (Watford).
Substitution, Watford. Christian Kabasele replaces Marc Navarro.
Attempt saved. Son Heung-Min (Tottenham Hotspur) right footed shot from a difficult angle on the left is saved in the bottom left corner.
Attempt missed. Ken Sema (Watford) left footed shot from a difficult angle on the left is high and wide to the left.
Attempt missed. Fernando Llorente (Tottenham Hotspur) header from very close range is too high.
Substitution, Tottenham Hotspur. Fernando Llorente replaces Lucas Moura.
Mousa Dembélé (Tottenham Hotspur) wins a free kick in the defensive half.
Foul by Will Hughes (Watford).
Substitution, Watford. Will Hughes replaces Kiko Femenía.
Foul by Erik Lamela (Tottenham Hotspur).
Ken Sema (Watford) wins a free kick in the defensive half.