Liam Walsh finished a classic counter-attack from the Toffees with just 10 minutes remaining of this Barclays Under-21 Premier League clash.
But we were level three minutes later as substitute Emmanuel Sonupe was brought down by Tom Davies and Andros Townsend fired home from the penalty spot.
The draw was the least we deserved after dominating for long periods with Townsend always a threat and Sonupe making an impression off the bench in the final 20 minutes.
Townsend was joined by Harry Winks, Shaq Coulthirst and Milos Veljkovic in the line-up as Ugo Ehiogu made just one change to the side that lost to Southampton seven days ago with Harry Voss coming in for Tom Glover in goal.
But we had to withstand early pressure as Everton pushed us back in the first 15 minutes.
Sam Byrne hit an early chance straight at Voss and the goalkeeper did well to palm out Matty Foulds' corner under pressure on the goal-line, before Davies screamed the loose ball just over.
Callum Connolly's shot from the next corner was guided over by Jordan Thorniley, Voss was forced into a flying punch to clear Foulds' inswinging free-kick and then darted off his line to collect at the feet of Leandro Rodriguez.
That all came in the first 15 minutes but we settled down after that and bossed the rest of the half in terms of possession and territory.
Chances were hard to find though. Coulthirst fashioned a spectacular backwards flick at goal from Townsend's cross on 17 minutes but despite getting in some good positions, we had to wait until the 44th minute for our first effort on target. Townsend darted between Foulds and Conor McAleny into the box, allowing Coulthirst to spin and fire in a shot that Mateusz Hewelt parried away to his left.
Everton had the final chance of the half as Harry Charsley's shot was blocked by Veljkovic and Byrne sliced the follow-up over.
The rain was really swirling around the stadium as the second half kicked-off and we were soon on the front foot.
The first chance of the half arrived on 52 minutes as Townsend beat Foulds and zipped a pass in to Coulthirst, who used the pace of the ball to beat Mason Holgate with his first touch - only to blast over from 16 yards. Townsend's shot was then half-blocked and Coulthirst was inches away from reaching the loose ball.
Everton then carved out two chances against the run of play. The first came from nothing, a free-kick awarded centrally 30 yards out that Connolly pinged low at goal, the ball cannoning back off the post. Rodriguez then headed over from Foulds' cross, 69 on the clock.
Sonupe replaced Anthony Georgiou just after that chance and had an opportunity to score himself within four minutes. Kyle Walker-Peters picked him out cross-field and Sonupe took the ball in his stride, sped past Connolly - only to by denied one-on-one by Hewelt from the left angle.
Everton hit us with a counter-attack to take the lead on 80 minutes. Townsend's cross was cleared and McAleny took off, sprinting fully 60 yards to the edge of our box where he played in substitute Walsh, who slid home from close range.
We responded inside three minutes, though. Sonupe showed great pace again down the left and was caught in full flight by Davies. Referee Paul Graham pointed to the spot and Townsend made no mistake, drilling low into the corner.
We continued to push for the win but that was the last of the chances.
Everton U21s: Hewelt, Connolly (Walsh 75), Foulds, Davies, Thorniley, Holgate, Charsley, Williams, Byrne (Dowell 62), Rodriguez (Evans 69), McAleny. Substitutes (not used): Dyson, Gray (GK).
Spurs U21s: Voss, Walker-Peters, Amos, Lesniak, Carter-Vickers, Veljkovic (c), Townsend, Winks (Miller 77), Coulthirst, Walkes, Georgiou (Sonupe 69). Substitutes (not used): Hayford, McDermott (GK).