Son Heung-min was the star of the show for Spurs on the day as he netted his first hat-trick for the club and showed that he can do it when it matters, especially after an early injury to star striker Harry Kane.
Christian Eriksen opened the scoring for the hosts on the day with Dele Alli and Vincent Janssen scoring the other goals for Mauricio Pochettino's side - who are into the final four of this competition for the first time since 2011-12
Spurs start strong but lose Kane to injury
As was expected, Spurs started the game on the front foot with Harry Winks forcing Tom King into a good save early on.
Minutes later, Kane was also denied by King. During the shot though, Kane went over on his ankle and had to be replaced - which will be a huge worry for everyone at Spurs, given the fact it is the same injury that kept him out for seven weeks earlier in the season.
When Kane went off, Spurs slowed down a bit and really struggled to break down a very well organised Lions defence until a moment of magic opened the scoring.
Eriksen puts the hosts into the lead
Eriksen, who came on as a substitute for the injured Kane, hit a fantastic strike into the bottom corner of the net on the turn after the visitors failed to clear the ball in the box just after the half-hour mark.
The hosts got a big lift from the opening goal and almost made it two when Victor Wanyama saw a header come back off the bar from an Eriksen corner.
Son's splendid strike makes it 2-0 before half-time
Pochettino's side did get a second goal though before half-time when Son was presented the ball by Eric Dier on the break and just as everyone thought the chance had gone, the winger produced a wonderful left-footed strike from just inside the box which flew straight into the top corner of the net, leaving King with no chance.
The hosts went in with a deserved 2-0 lead and if Millwall were going to get back into the game, they needed to score the next goal.
Son scors his second early in the second-half
Unfortunately though Spurs were in no mood to stop scoring as Eriksen forced King into yet another good save from the edge of the box.
The third goal eventually came when Kieran Trippier's brilliant long pass found Son, who on the volley, put the ball into the back of the net for his second goal of the game.
The Lions though should have pulled one goal back when Fred Onyedinma, on as a second half substitute, played a good pass into the box to Jed Wallace, who put his shot over the bar when he should have done so much better.
Alli scores customary goal to make it four for the hosts
Apart from that chance though the visitors created very little. Spurs though were not finished and got their fourth goal of the game when Eriksen found Alli unmarked at the back post to tap the ball into the net.
Vincent Janssen nets his first open play goal for Spurs
It was five soon after when Janssen, who came on as a second-half substitute, scored his first goal for Spurs from open play as the North London side ran riot against their capital rivals.
The Dutch striker should have had a second moments later when Ben Davies found him unmarked in the box but he put his header straight at King.
Son completed his hattrick before the end to send Spurs to the semi-finals
Just as it looked like the scoring was finished, Spurs got a sixth goal with the last kick of the game, when Eriksen found Son, who saw his shot somehow go into the net through King's legs to net his first hat-trick for Spurs and send Spurs to the semi-finals.