The striker produced two fine finishes and was calmness personified as he went through on goal, clipping both goals home as Villa goalkeeper Benji Siegrist advanced.
A draw was no less than the team deserved from an entertaining clash at the Lane and the coaching team will no doubt point to defensive errors that cost them dearly on the night.
Villa were always dangerous though and in Jordan Bowery and Graham Burke had a front pair ready to capitalise.
The game couldn't have started any better for the lads in white.
Dean Parrett had already tested Siegrist from distance when Obika opened the scoring on four minutes.
The goal owed a lot to Milos Veljkovic's crunching tackle in central midfield, Parrett released Obika in an instant and the striker coolly dinked over Siegrist as the goalkeeper went to ground.
Bowery forced a routine save from Jonathan Miles to his right before Adam Smith did well to deny the big Villa front man as he pulled the trigger.
Smith's bursts forward caught the eye and he went close on 23 minutes, leaving three Villa players in his wake before drilling just wide.
Obika didn't get enough on an attempted lob from Parrett's pass but then a huge chance wasted for Villa as Burke somehow failed to connect with Daniel Johnson's cross in front of goal.
Smith and then Pritchard kept Siegrist on his toes with efforts from distance before Villa capitalised on a rare wayward pass from Parrett to equalise on 37 minutes. Bowery played the right pass into Burke who curled home from 20 yards.
The visitors soon had the chance to take the lead as Samir Carruthers broke through centrally and placed his effort high past Miles, the ball clipping the top of the crossbar on its way into Park Lane.
An entertaining half ended with two further chances for us. Parrett and Obika opened it up for Carroll to fire over before Obika nutmegged Danny Devine before aiming his shot across Siegrist and just wide.
The second half was no less lively and Miles was soon forced to palm away Derrick Williams' free-kick.
Two minutes later and we'd regained the lead. This was all down to Parrett's fantastic cross from the right after Pritchard took a quick free-kick. The cross just needed directing on target and Kevin Stewart was on hand to finish, 52 minutes on the clock.
The lead only lasted six minutes though. Stewart misjudged a long clearance down the left channel and Burke was there to pick up the pieces, squaring for Bowery to convert from close range.
Villa took the lead for the first time after 67 minutes as Miles lost the flight of Carruthers' deep, inswinging free-kick from the left and the ball found its way into the far corner.
Obika carved out the next chance, using his strength to release Nabil Bentaleb on goal. Siegrist did well to save the initial effort and Josh Barton even better to block on the line as Obika followed up.
It wasn't long though before Obika found the equaliser, latching onto Giancarlo Gallifuoco's pass and producing a carbon-copy finish to his opener, clipping the ball over Siegrist.
We had two chances to win it as Pritchard troubled Siegrist from distance and then Obika was inches away from Smith's superb cross, with Gallifuoco following up at the far post but firing over.
Spurs U21s (4-2-3-1): Miles; Smith, Hall, Stewart, Barthram; Veljkovic, Carroll (Munns, 68); Bentaleb (Gallifuoco, 80), Parrett, Pritchard; Obika. Unused subs: Priestley, Dombaxe.
Villa (4-4-2): Siegrist; Herd, Devine, Baker (Cameron, 11), Williams (Barton, 46); Carruthers, Westwood, Johnson, Stieber; Bowery (Drennan, 78), Burke. Unused subs: Barrett, Barton, Grealish.