You always felt the team carried the greater goal threat on what was at times a cagey encounter and both Georgiou and Azzaoui took their chances in great style to set-up a quarter-final away to Nottingham Forest.
Azzaoui's goal was the pick of the bunch after great work from Josh Onomah and he now has five goals in our three ties so far against Blackburn, Wolves and now United.
The first half took time to get going as the teams worked each other out.
Azzaoui provided the spark from the left and carved out the first chances, a dangerous cross aiming for Shayon Harrison cut out and then a shot deflected wide in the 15th minute. The ensuing corner was half-cleared, Azzaoui lofted the ball back in and Christian Maghoma climbed high to beat Dean Henderson in the air, his header just wide.
Maghoma was in the opposition box again five minutes later, this time darting in at the near post to try and meet Harrison's cross. That lead to the opener as Azzaoui's low corner was flicked on by Anton Walkes and Georgiou volleyed home from close range for 1-0.
The lead only lasted five minutes. We were called for a foul 30 yards from goal and Marcus Rashford curled the free-kick over the wall and into the bottom corner.
As the intensity upped a level, there was one more chance of note as Harrison's low strike from 20 yards was turned away down to his left by Henderson.
United pushed further onto us at the start of the second half, looking to stop us playing out from the back and getting players around Onomah.
The first 15 minutes were pretty scrappy with Georgiou's volley from Azzaoui's corner the only chance of note on 49 minutes.
The game came alive again on the hour. Georgiou had a shot blocked, Anton Walkes headed onto the roof of the net and at the other end, Cameron Borthwick-Jackson's goal was disallowed for offside.
Onomah was pivotal to the crucial second goal. Picking up the ball deep in our half, the midfielder broke forward fully 50 yards, played a one-two with Georgiou and then calmly rolled into Azzaoui, who finished in style, chipping over the advancing Henderson.
The chances were flowing now as Cameron Carter-Vickers headed just over and last-ditch blocks denied Harrison twice and Onomah in front of goal.
Tyler Reid managed to relieve the pressure on United with a solo run and shot well saved by Harry Voss but you sensed a third was on its way and it duly arrived on 71 minutes.
Kyle Walker-Peters released Georgiou down the right and his raw pace took him away from Borthwick-Jackson and into the box where he kept his cool and finished low past Henderson.
Marcus Edwards, Kazaiah Sterling and Charlie Owens all came off the bench inside the final 15 minutes and Sterling twice tested Henderson on the 85-minute mark.
United had a couple of shots from distance easily fielded by Voss, Edwards slid a shot just wide and it was a feeling of a job well done on the final whistle.
Spurs: Voss, Walker-Peters, Walkes, Amos, Maghoma, Carter-Vickers, Georgiou, Stylianides (Owens, 83), Harrison (Sterling, 79), Onomah (c), Azzaoui (Edwards, 73). Substitutes (not used): Loft, Glover (GK).
Manchester United: Henderson; Reid, Tuanzebe (C), Williams, Borthwick-Jackson; Fosu-Mensah, Redmond; Riley, Gribbin, Dearnley (Mitchell, 72); Rashford. Substitutes (not used): Thompson, Croskery, Scott, Dorrington (GK).