The striker launched himself to meet Cristian Ceballos' cross in the 89th minute of a thrilling play-off semi-final at White Hart Lane.
It means the lads, who won both National Group Two and Elite Group in the first two phases of the new competition, will get the chance to win the overall title against either Manchester United or Liverpool, who play on Tuesday night.
The final was drawn as an away match for us and the date is to be confirmed.
Obika joined Tom Carroll, Alex Pritchard and Jordan Archer in the starting line-up, while the Toffees fielded experienced goalkeeper Jan Mucha and Ross Barkley, who has earned rave reviews in the first team of late.
Once again backed by superb support, we started brightly and after Obika was blocked 50-50 by Mucha from Nabil Bentaleb's pass, we opened the scoring in the 11th minute.
Carroll looked for Pritchard over the top, John Stokes read it and looked to nod back to Mucha but didn't get enough on the header and Pritchard was able to nip in and stroke home.
Archer made a sharp save to his left to deny McAleny and Mucha was soon in action again, this time low down to his left to turn away Obika's drive after the striker had been sent clear by Milos Veljkovic.
Luke Garbutt curled a free-kick just wide on 29 minutes and the Toffees levelled in the final seconds of the first half as Stokes whipped in a low cross and McAleny turned on a sixpence to fire low into the corner from 12 yards.
The teams exchanged goals at the start of the second half - with Stokes involved again at both again.
First of all, the right-back lost possession to Obika on the edge of the Everton box and Obika made no mistake, steadying himself before tucking into the corner.
But the lead lasted just two minutes. Stokes was there again, his cross from the right collected by Chris Long, who controlled and hooked the ball over his head, over Archer and into the far corner.
The goal clearly buoyed the visitors and they enjoyed their best spell. Archer did well to touch the ball wide after Garbutt's cross was deflected on target by Ceballos on 56 minutes, Shane Duffy headed Barkley's corner wide and then Long struck the foot of the post from the right angle.
We were soon on the front foot again as Mucha somehow denied Obika, who slid in to meet substitute Kenny McEvoy's cross. Obika was a matter of yards out on connection but Mucha diverted the ball away, it might have even hit him on the head!
Back came Everton and Barkley met Garbutt's cross, only to head inches wide, 79 minutes on the clock.
Obika stretched to reach McEvoy's cross but couldn't keep it on target but he made no mistake in the final minute, stooping low to meet Ceballos' cross and guiding the ball into the corner.
Typical of the match, Everton carved out a final chance to equalise in added time, but Archer was up to the task, diving spectacularly to turn away Long's flick towards the goal from the near post.
Spurs U21s (4-3-3): Archer; Fredericks (Barthram, 56), Hall, Stewart, Fryers; Bentaleb (Gallifuoco, 90), Carroll, Veljkovic; Pritchard (McEvoy, 76), Obika, Ceballos. Unused subs: Miles, Nicholson.
Everton (4-2-3-1): Mucha; Stokes, Duffy, Browning, Garbutt; Lundstram, Grant (Waring, 90); Long, Barkley, Kennedy (Duffus, 18); McAleny. Unused subs: Springthorpe, Duffus, Green, Pennington.