There was nothing in it for an hour as our well-drilled line-up - set up with three central defenders - comfortably kept the leaders at bay.
Will Miller, Filip Lesniak and Cy Goddard covered every blade of grass as chances were few and far between. The best fell to Shilow Tracey, who was denied one-on-one by Mateusz Hewelt.
The second half followed the same pattern until the hour mark, when Everton's opener sparked that four-goal spell.
Ademola Lookman nudged home the first goal at the far post and Bassala Sambou soon doubled Everton's lead with a curler into the top corner.
It looked tough from there but we responded on 72 minutes when Marcus Edwards worked a yard in the box and his effort looped into the path of Kazaiah Sterling, who headed home from a yard out.
The wind was taken out of our sails just three minutes later when Kieran Dowell found another fine finish from 20 yards and Everton finished it off from our defensive mistake three minutes from time, Dominic Calvert-Lewin taking advantage 12 yards out.
FIRST CHANCE OF NOTE: EDWARDS CLOSE - 26mins
Chances were few and far between in the early stages. Dowell chipped a yard over, Tracey did well to fashion an effort from the right angle and Edwards fired a free-kick over from 30 yards. The first serious chance arrived on 26 minutes when Edwards dribbled into the box from the left, only for Brendan Galloway to block his shot from 10 yards.
CHANCES: BOTH SIDES CLOSE - 34-41mins
Goddard took a quick free-kick that saw Tracey get goal-side of Morgan Feeney and through on goal from the left angle, he looked to place across Hewelt who blocked the shot one-on-one. Christian Maghoma rose well to meet the ensuing corner but headed over. Everton hit back as Calvert-Lewin headed wide from Lookman's cross. Maghoma then just failed to connect with Miller's corner before Lookman and Joe Williams had shots blocked in the box.
Above: Jaden Brown is tackled.
GOAL: EVERTON 1-0 SPURS - ADEMOLA LOOKMAN - 61mins
The second half followed a similar pattern to the first with the defensive shape of both teams making creating chances difficult. Lookman had a shot blocked by Maghoma and Tracey headed over before the home side forged ahead. It took a break from deep by Galloway to open us up, his cross from the left evaded everyone and reached Lookman to turn home at the far post.
SAVE: MILLER DENIED BY HEWELT - 63mins
We almost found the perfect response as Tracey drove into the box before rolling back to Miller, whose attempted curler to the far post was tipped wide at full stretch by Hewelt.
GOAL: EVERTON 2-0 SPURS - BASSALA SAMBOU - 69mins
Sambou came off the bench for Everton on 64 minutes, had a shot blocked with his first touch and then went one better, picking up the ball 20 yards out, turning and curling into the top corner for 2-0.
GOAL: EVERTON 2-1 SPURS - KAZAIAH STERLING - 72mins
Another substitute to make an impact, this time Edwards twisted left and right on the left side of the box, his shot was blocked and looped up into the path of Sterling, who nodded home from close range just four minutes after coming on for Miller.
GOAL: EVERTON 3-1 SPURS - KIERAN DOWELL - 75mins
Our hopes of getting back into the game lasted three minutes as Everton found a carbon copy of the second goal. This time Dowell cut in from the right and was running out of options, so he took the best one - a left-foot curler into the top corner.
GOAL: EVERTON 4-1 SPURS - DOMINIC CALVERT-LEWIN - 87mins
A poor defensive clearance left Calvert-Lewin with the easiest of tasks to round off the scoring from 12 yards with three minutes of normal time remaining.
COACH UGO EHIOGU SAID
"There were five shots on target and they scored four, but for 65 minutes I thought we controlled the game if I'm being honest. We lacked a killer instinct, a bit of power and directness at times, plus a bit of cuteness - they were a bit cuter than us and played with a bit more football nous and league experience than we did. We were a little bit too honest in that respect.
"If Shilow Tracey scores his chance then it's a different game but football is about chances and we didn't take ours - the set-piece headers, the one-on-ones - but they did. The third goal was a big blow really but for work rate and honesty, I don't think we can fault the boys. Cy Goddard and Filip Lesniak were very good and Christian Maghoma was very authoritative with good use of the ball, his defending and a good voice. Jaden Brown has done himself good - in the main he showed flashes of what he can do, athletically and in terms of adventure but he's got to play with more intensity in and around the final third. The boys have got to get used to that.
"Marcus Edwards, at times, went past players at will but the one criticism was that he wasn't ruthless and didn't get shots off. On the whole it was a lesson in that extra little bit of power and experience. In the crucial 60- to 90-minute period, it's certainly in your mind that you've got to dig in and stay within the game - that's the barrier for me that decides between boys' football and men's football."
Everton: Hewelt, Kenny (c), Robinson, Besic (Charsley 46), Feeney, Galloway, Dowell (Henen 84), Walsh, Calvert-Lewin, Williams, Lookman (Sambou 64). Substitutes (not used): Gray (GK), Foulds.
Spurs: Glover, Eyoma, Tanganga, Lesniak (c), Maghoma, Johnson (trialist, Bennetts 77), Miller (Sterling 68), Goddard (Marsh 81), Tracey, Edwards, Brown. Substitute (not used): Whiteman (GK).
Goals: Everton - Lookman 61, Sambou 69, Dowell 75, Calvert-Lewin 87; Spurs - Sterling 72.
Yellow cards: Spurs - Johnson 76.
We travel to Old Trafford to face Manchester United in our penultimate match of the Premier League 2 campaign on Monday, April 24 (7pm).