We struck the woodwork twice through Souleymane Coulibaly and Laste Dombaxe and the excellent Harry Kane was denied by the save of the night from Mason Springthorpe in the Everton goal, a fantastic reaction stop to his right to turn away a piledriver in the second half. Had one of those efforts found the net, you felt we'd have gone on to win the game.
also excelled when called into action as the Toffees created a few chances, most notably a save in each half from Luke Garbutt and Joe Williams.
The first half burst into life from the off with four chances inside the opening 10 minutes.
We had three, with Coulibaly striking the post from 25 yards after three minutes before heading wide from Kenny McEvoy's cross. Kane then fired just wide from 25 yards.
In-between, at the other end, Hallam Hope latched onto a loose ball in the box, only to prod wide from close range.
Archer was called into action on 16 minutes, a full-stretch tip over from Luke Garbutt's dipper, but the goalkeeper could do little when George Green drilled to the far post five minutes later, this time Dominic Ball got back to clear off the line.
Both teams looked to attack at pace and Kane went close again on the half-hour, a clever glancing header from Shaq Coulthirst's cross forced a fine save from Springthorpe, who backpeddled to palm the ball wide.
The next 15 minutes were slightly quieter and the final chance of the half fell to Coulibaly after good work from Kane and Coulthirst, his low shot from close range deflected just wide with Springthorpe beaten.
Laste Dombaxe replaced Zeki Fryers at half-time and stepped into midfield with Alex McQueen shifting to left-back and Aaron McEneff back to right-back.
We had the first chance of the half on 56 minutes as Milos Veljkovic worked a short corner with McEvoy, his cross cleared to Ball, who powered his header wide from 16 yards.
Kane lashed wide from 30 yards after taking Coulibaly's knockdown in his stride and then forced a fine save from Springthorpe on 70 minutes. Breaking from deep, Kane used McEvoy's run to open up space and blasted at goal from the edge of the box, but Springthorpe was equal to it.
McEvoy's pace caught the eye as time ticked away and Kane looked a constant threat, his next effort on 78 minutes deflected and dipped just over. From the corner, the ball was cleared to Dombaxe, who ripped a full volley that clipped the top of the crossbar.
We made a double switch with 10 minutes remaining, Darren McQueen and Ruben Lameiras on for Gallifuoco and Coulibaly and a tactical switch to three at the back, searching for the winner.
Archer made a fine save low down to his right to deny Williams in a rare Everton attack and from the corner, Matthew Pennington headed just wide.
The last chance arrived in the final seconds, Garbutt left a backpass short and Coulthirst chased it down but Springthorpe just got there first to clear.
Spurs U21s: Archer; A McQueen, Ball, Gallifuoco (D McQueen, 79), Fryers (Dombaxe, 46); McEneff, Veljkovic; Kane; Coulibaly (Lameiras, 79), Coulthirst, McEvoy. Unused subs: McGee.
Everton: Springthorpe, McLaughlin, Garbutt, Ledson, Pennington, Browning, Green (McAleny, 59), Williams, Hope (Charsley, 76), Kennedy, Duffus (Touray, 90+2). Unused subs: Griffiths, Langton.