Trailing 2-0 at half-time despite dominating the first half, the deficit was halved on 62 minutes when Georgiou - introduced just six minutes earlier - drilled home from the left angle.
It was all-square five minutes from time when Kane Vincent-Young crossed from the right byline and Georgiou volleyed into the ground and into the far corner.
There were still chances after that but West Brom goalkeeper Alex Palmer parried out Connor Ogilvie's rasper on 90 minutes and then Georgiou fired across goal, Palmer palmed out and the ball agonisingly ran away from Kyle Walker-Peters in front of goal.
Palmer made a number of fine saves and as chances came and went, West Brom took advantage to take a 2-0 lead into the interval.
Daniel Akindayini and Harry Winks went close before the visitors struck on 15 minutes, Jonathan Leko's drive from the edge of the box appeared to take a slight deflection on its way to the bottom corner.
Palmer tipped over from Onomah and Akindayini was denied in front of goal after good work down the right from Emmanuel Sonupe, who then fired over from the right angle.
Cameron Carter-Vickers won possession deep in West Brom territory on 40 minutes and poked the ball to Sonupe, who forced a brave save from Palmer. The goalkeeper did even better to turn away Harry Winks' drive from 20 yards a minute later but just as you thought the equaliser had to come, the Baggies broke away and doubled their lead.
This time, Samir Nabi cut in from the left and curler a 20-yarder across Luke McGee into the bottom corner.
Sonupe had the first effort at goal five minutes into the second half and on a rare attack, McGee did well to block one-on-one from Tahvon Campbell.
Georgiou replaced Nathan Oduwa on 56 minutes and we were back in the game on 62. Will Miller slid Georgiou on down the left and his crisp drive beat Palmer at the near post.
It was completely one-way traffic now. Baggies defender Kyle Howkins did well to block from Georgiou in front of goal, Georgiou was inches away from Akindayini's shot after good work from Walker-Peters, Josh Onomah tested Palmer.
The next action saw a goal disallowed. Palmer saved Ogilvie's blaster and was up to deny Walker-Peters and Akindayini before Ogilvie finally tapped in - but the flag was up for an earlier foul.
Onomah then turned Winks' free-kick onto the post.
The lads kept going and were rewarded five minutes from time. Walker-Peters and Vincent-Young combined down the right, Vincent-Young got to the byline and stood up a cross for Georgiou to dispatch at the far post.
That was the least the performance deserved - the lads now prepare for their FA Youth Cup fourth round tie against Fulham at Dagenham & Redbridge on Thursday (7pm).
Spurs: McGee; Vincent-Young, Carter-Vickers, Lesniak, Ogilvie; Miller, Onomah, Winks; Sonupe (Walker-Peters, 71), Akindayini (Pritchard, 78), Oduwa (Georgiou, 56). Unused sub: Voss.
West Brom: Palmer, Donnellan, Greendiue, Cleet (Gannon, 67), Howkins, Jones, Ward (Wedderburn, 46), Leko, Oldnall (Campbell, 59), Wright, Nabi. Unused subs: Ezewele, Ross.
Below - Emmanuel Sonupe fires in a shot in the first half...