The striker was central to a dominant second half display after Villa had the better of the first half and deservedly led 1-0 at half-time.
As well as the penalty three minutes into the half, Kane and Laste Dombaxe struck the post and Villa goalkeeper Benjamin Siegrist produced a string of fine saves.
Jordan Archer had to be at his best in the first half as we struggled to find our rhythm.
Our best chance arrived on three minutes when Kane broke down the right and his cutback found Simon Dawkins, who made sure he hit the target but saw his effort blocked by Joshua Webb.
Villa took the lead on 18 minutes. Daniel Johnson whipped in the corner from the right and Kevin Toner threw himself in to power his header home from 10 yards.
We responded well to that setback. Dombaxe curled straight at Siegrist, Shaq Coulthirst turned Kenny McEvoy's cross on goal but was blocked by Janoi Donacien and McEvoy darted onto Dawkins' pass into the box and poked past the outrushing Siegrist but wide.
Archer was at full stretch to turn away Johnson's piledriver on 36 minutes and did even better to tip over Andras Stieber's free-kick a minute before the break.
Cameron Lancaster was introduced at half-time for Coulthirst and the second half was a different story.
Kane ran the show as we pinned Villa back. The striker released Lancaster on goal on 47 minutes, the one-on-one blocked by Siegrist and was then upended by Toner in the box, picking himself up to smash the ball down the middle of the goal for 1-1.
Kane and Bentaleb opened it up for McEvoy, denied again by Siegrist and the winger then picked out Bentaleb, who rifled just over from 16 yards.
There was a warning at the other end as Villa almost capitalised on a loose pass, Johnson's low drive rebounding off the foot of the post.
Play switched straight up the other end as Siegrist denied Kane from the left angle and from the corner, the ball was cleared to Dombaxe who connected sweetly with a volley that cannoned back off the inside of the upright.
The chances continued to flow. Lancaster cleared the bar from McEvoy's cut back, Bentaleb's fierce drive was palmed out by Siegrist and then Kane worked a one-two with Lancaster and looked odds-on to score, only for Siegrist to touch the ball onto the post.
Villa carved out a golden chance in the 83rd minute when Calder broke into the box and rolled to substitute Thomas Strain, who couldn't turn the ball home from close range.
McEvoy and Lameiras delivered a number of crossed in the final five minutes but the winner remained elusive on this occasion.
Villa U21s (4-4-1-1): Siegrist; Webb, Donacien, Toner, Kinsella; Stieber (Strain, 67), Cowans (O'Brien, 67), Lyden, Calder; Johnson; Sellars. Subs not used: Wildin, Watkins, O'Brien, Abdo.
Spurs U21s (4-2-3-1): Archer; A McQueen, Ball, Veljkovic, Fryers; Bentaleb, Dombaxe (Lameiras, 73); McEvoy, Kane, Dawkins; Coulthirst (Lancaster, 46). Sub not used: Vigouroux.
Goals: Villa - Toner (18). Spurs - Kane (penalty, 48).
Referee: Mr A Tankard.