Ben Davies opened the scoring for the hosts 19 minutes before the end of the game with a glancing header to score his first ever goal for the hosts.
Heung-Min Son added a second for Spurs before the end of the game which sees them go into the hat for the fourth round draw which takes place on Monday evening.
Poor first half sees very little chances
Mauricio Pochettino made nine changes to his Spurs side for the game with the likes of Harry Kane, Christian Eriksen and Dele Alli not in the starting eleven.
It showed throughout the first half as the hosts struggled to create anything of note as the visitors defended in numbers at the back which made if difficult for the hosts to create chances.
It was clear to see how Steve Bruce had set out his Villa side during the game as he wanted his side to soak up all of the pressure and try to catch the hosts on the break.
The only shot on target in the first half came from the visitors when Leandro Bacuna forced Michel Vorm into a decent save from a long way outside the box.
As the half went on, the crowd started to become very restless as the players who haven't played as much this season for the hosts was struggling to make an impact.
Overall Pochettino would have been hoping for so much more from his side in the first half as they failed to show what they could do in a poor half of football in truth.
Hosts started much better at the beginning of the second half
The second half was much better as Spurs started the second half much brighter and created their first meaningful chance just as the half began as Vincent Janssen forced Sam Johnstone into making a smart save.
Son was next to go close for the hosts not long after that after a long ball over the top played him in on goal but he saw his first time shot well saved by Johnstone, who was starting to become a very busy keeper in goal.
Davies and Son secure passage through to the fourth round with two goals in nine minutes
Just as it looked like it would be one of them afternoons for Spurs, they finally got the breakthrough in the 71st minute of the game.
Georges-Kevin N'Koudou, who had just came on as a second half substitute, created the goal as he put a brilliant cross into the box and Davies headed the ball into the back of the net to score his first ever goal for Spurs.
From there it was a formality for Spurs as they had finally worn down the visitors and they managed to get a second goal nine minutes after the first as Son stroked the ball into an empty net after a good run and cross from Moussa Sissoko.
The hosts had further chances to score even more goals as both Sissoko and Son saw shots well saved by Johnstone before the end but it didn't matter as they made it safely through to the fourth round of the FA Cup.