Jack Munns capped a fine display with two goals with Zeki Fryers and Laste Dombaxe also on target. Munns was involved in all four goals, including being brought down for Dombaxe's penalty.
Arsenal looked like they might run away with it after taking an early lead and creating a number of chances in the first 20 minutes.
The tide turned with two goals in as many minutes before half-time and the team's best spell was rewarded with Munns' goal for 3-1 10 minutes into the second half.
However, Chuba Akpom capitalised on a mistake for 3-2 and Jonathan Miles had to rescue his own mistake with a superb save in the 90th minute to keep it that way.
We still hadn't finished though as we broke away to secure the win with Munns tapping home from close range for 4-2. And there was still time for Nathan Byrne to clear off the line and Arsenal to hit the crossbar!
It was a notable win for the Under-21s, who have lost the services of the likes of Ryan Mason, Yago Falque, Alex Pritchard, Jon Obika and Harry Kane in recent weeks, all key players who have now gone out on loan.
The result also stretched the team's record to five wins and a draw from six games in the second phase of the Barclays U21 Premier League and they top the Elite Group.
It looked like it might be a long afternoon for the new-look team as the Gunners dominated the early exchanges.
Miles was forced to make a couple of vital early saves, standing up well to block from Akpom after the striker raced clear but the goalkeeper could do little as the same player curled into the corner to open the scoring on 10 minutes.
Zak Ansah then struck the underside of the crossbar from Serge Gnabry's cross and Miles was there when Akpom was first to the rebound to block with his feet from point-blank range.
Ansah should have done better from 12 yards after 17 minutes but there was a shift in momentum half-way through the half.
Dombaxe's shot from Munns' cutback was blocked by Ignasi Miquel and Munns was involved again as we levelled after 28 minutes, his cross from the right half-cleared to Fryers, who provided the calmest of sidefoot finishes from the edge of the box.
A minute later and Munns was tripped by Miquel in the box and Dombaxe - who scored in our NextGen Series penalty shoot-out win against PSG in midweek - did the trick again from the spot, slotting into the corner for 2-1, 31 minutes on the clock.
Munns showed quick feet again to turn Sead Hajrovic before firing straight at Fabianski and in the final action, Dean Parrett curled a free-kick just wide from 30 yards.
The management team made two changes at half-time with Nabil Bentaleb and Dominic Ball on for Milos Veljkovic and Kevin Stewart.
Miles was there again to palm away Gnabry's fierce shot on 52 minutes before we enjoyed a purple patch for 10 minutes.
The third goal arrived in that time and owed much to Bentaleb winning possession and finding Kenny McEvoy wide right. He did well to fizz in a low cross that was only cleared to Munns, who buried from close range.
McEvoy cushioned Fryers' crossfield pass into the path of Byrne, whose shot was destined for the top corner before Lucasz Fabianski tipped away. Munns then turned Miquel again, but fired straight at Fabianski.
The lads looked in control but allowed the Gunners back into the game in the 63rd minute when Giancarlo Gallifuoco lost possession to Akpom, who finished one-on-one.
McEvoy delivered another couple of dangerous crosses before being replaced by Mason Bush and there was a relatively quiet spell before the game exploded in the final minutes.
Fabianski turned Bentaleb's shot away at the near post with four minutes left and then in the 90th minute, Miles kicked straight to Josh Rees, who was through on goal. Thankfully, Miles was up and able to touch Rees' effort inches wide, a fine save.
Two minutes later and it was all over as Parrett released Bush, his shot was saved by Fabianski but Munns was there to touch home the rebound for 4-2.
There was still time for Byrne to spectacularly clear Akpom's lob off the line and for Akpom to head against the crossbar from the corner, but there could be few arguments as to the destiny of the points as the whistle blew seconds later.
Spurs U21s: Miles; Byrne, Gallifuoco, Stewart (Ball, 46), Fryers; Dombaxe, Luongo, Veljkovic (Bentaleb, 46); Parrett, Munns, McEvoy (Bush, 74). Unused subs: Vigouroux, Miller.
Arsenal: Fabianski; Bellerin, Hajrovic, Miquel, Angha; Ansah (Rees, 74), Hayden, Olsson; Henderson, Akpom, Gnabry. Unused subs: Shea, Wynter, Monteiro, Neita.