We could have been long gone by the time Adam Morgan gave the home side that brief lifeline.
We created five goalscoring opportunities after Ceballos' made it 2-0 but failed to find the third goal.
Morgan's goal represented Liverpool's first shot in the second half and they struck the woodwork seconds later as Joao Teixera broke through.
An equaliser would have made for an interesting final 20 minutes but anything other than a Spurs win would have been a travesty.
Thankfully, McEvoy drilled home from the right angle to make the final scoreline more of a reflection of the 90 minutes.
It stretched the team's record to eight wins, a draw and defeat in 10 matches in the second phase of the Barclays U21 Premier League.
All this with a young team - eight Academy trainees featured and six started - and 13 players currently out on loan who have played for the Under-21s this season - Adam Smith, Yago Falque, Souleymane Coulibaly, Alex Pritchard, Ryan Mason, Andros Townsend, Harry Kane, Jon Obika, Jonathan Miles, Kevin Stewart, Massimo Luongo, Dean Parrett and Nathan Byrne.
Laste Dombaxe and Nabil Bentaleb went close before Liverpool's only chance of note in the first half as Krisztian Adorjan's effort from Kristoffer Peterson's cutback appeared to be missing the target, but was blocked anyway by Ryan Fredericks.
Peter Gulacsi produced a fine save to turn away Shaq Coulthirst's header from Ceballos' whipped corner on 20 minutes and it was soon 1-0 as Ceballos tricked his way past Ryan McLaughlin on the left byline and fired across goal, his cross cannoning home off Gulacsi.
Ceballos and Dombaxe both went close from the edge of the box as we ended the first half on top.
That dominance stepped up a level in the second half and it was no surprise when Ceballos struck again for 2-0 on 51 minutes.
This was a fine goal, started by Milos Veljkovic's pass wide to Jack Barthram on our left. He played into the box to Coulthirst, who held the ball up and played it back out to the full-back. Barthram delivered again and Ceballos was there to head home from eight yards.
That sparked the best 15 minutes of the match.
Ceballos had a shot blocked in front of goal from McEvoy's cutback and McEvoy then took off on a 50-yard run before rolling the ball into Coulthirst, who blasted over.
Veljkovic hit a crossfield pass to Ceballos, who crossed for Coulthirst at the near post, the striker this time flicking over. Ceballos then cut inside Craig Roddan only to fire into the side-netting.
The best chance arrived for Veljkovic on 65 minutes as the midfielder timed his run into the box to perfection to meet McEvoy's cross, only to power his header over from 12 yards.
After all those chances, it was Liverpool who broke clear to score the next goal.
Morgan raced onto a pass over the top, skipped around the advancing Lawrence Vigouroux and then showed composure to step inside Ryan Fredericks and Grant Hall before slotting home.
Incredibly, it could have been 2-2 seconds later as Texeira broke through and clipped the top of the crossbar from 16 yards.
The lads settled again after that and the points were secured by McEvoy three minutes from time. The goal owed much to pressure on the ball from Zeki Fryers and Roman Michael-Percil, Dombaxe threaded through to McEvoy and he fired across Gulacsi into the far corner.
Vigouroux made a fine late save from Morgan's volley to keep it at 3-1 and the points certainly went to the right home.
Spurs U21s (4-3-3): Vigouroux; Fredericks, Fryers, Hall, Barthram (Ball, 84); Veljkovic, Dombaxe, Bentaleb; McEvoy, Coulthirst (Munns, 60), Ceballos (Michael-Percil, 84). Unused subs: Priestley, Lameiras.
Liverpool (4-3-3): Gulacsi; McLaughlin, Jones, Sama, Roddan; Teixera (Brannagan, 65), Coady, Adorjan (Nacho, 46); Peterson, Morgan, Ibe. Unused subs: Baio, Ward, Yukendi.
Cristian Ceballos struck twice and Kenny McEvoy clinched it at 3-1 after Liverpool pulled a goal back for 2-1 with 20 minutes remaining.