After Shayon Harrison saw his first half penalty saved by Mateusz Hewelt, we gifted possession to Henen with a little over 10 minutes remaining and the rapid Everton midfielder took full advantage to fire past Tom Glover from a tight angle on the left.
Substitute Foulds added the second from close range six minutes later after an initial good save from Glover, with our young side unable to find a way back into the game.
It all amounted to a frustrating night in the newly-rebranded competition, which has replaced the Under-21 Premier League.
OFF THE LINE: PRITCHARD KEEPS IT GOALLESS - 7mins
Everton's first real spell of pressure saw goalkeeper Glover - wearing a baseball cap as he faced the late evening Hertfordshire sunshine - turn Henen's cross over the top and from the resulting corner, Ryan Ledson stole ahead of his marker and powered a downward header towards goal, but Joe Pritchard was there to turn it away on the line.
SAVE: HEWELT DENIES HARRISON - 16mins
We were starting to impose ourselves on the game and after Will Miller's shot drifted wide of the far post, Marcus Edwards went on an arching run through the middle and sent Harrison through on goal, but Hewelt made himself big as he advanced off his line and was able to block as the striker tried to lift the ball over him.
PENALTY SAVED: HARRISON THWARTED BY HEWELT - 35mins
Gethin Jones was forced to put Miller's cross behind for a corner and from the resulting flag kick, Anton Walkes sought to pick up the pieces on the far side. As he did, he was tripped by Morgan Feeney and a penalty was awarded, but Harrison's low left-footed effort was kept out by Hewelt, stooping to his left.
Above: Joe Pritchard in action.
SAVE: GLOVER MAKES GOOD STOP IN GOALMOUTH SCRAMBLE - 60mins
We couldn't quite capture our rhythm after half-time and although Harrison coaxed a good save from Hewelt with an angled shot from the right side it was Glover who had to intervene after an Everton set piece routine. Brendan Galloway nodded a wide free-kick from the left back into the danger zone at the back post and Feeney attacked the ball purposefully but Glover was in the way, the keeper eventually gathering the ball at the second attempt after a scramble in the six-yard box.
GOAL: SPURS 0-1 EVERTON - DAVID HENEN - 79mins
As an even second half drifted on it was Everton who took the lead - but with a goal of our own making. A cross-field pass from Walkes fell short of its target and Henen sped forward down the left. The desperately retreating Amos was closest to him but, already on a yellow card, he knew he had to get his challenge right and ultimately Henen was able to burst clear of him. He surged into the box and lashed in from the left angle.
GOAL: SPURS 0-2 EVERTON - MATTHEW FOULDS - 85mins
The Toffees put the game beyond doubt when Foulds, who had an eventful ending to the game having been booked moments after his introduction off the bench, rushed in to sweep home the loose ball after Glover had made a good stop on his line to deny Courtney Duffus.
COACH UGO EHIOGU SAID
“You’ve got to take your chances. We had four excellent chances and when you're on top, especially when you're as dominant as we were in the first half - we missed a penalty, we missed two great one-on-ones - then you kind of think it’s not your day.
"At half-time the boys were a bit flat because they hadn’t scored, we talked about winning the second half defensively with a clean sheet and good, solid foundations but we've made some inexplicable decisions with the ball and we got punished severely for it. Even then I don’t think we smelt danger quick enough in our recovery, I thought some of our boys could have got in quicker.
"It's a learning curve in our first game of the season. It's frustrating and disappointing because on the first half I thought we deserved something out of the game. The boys have to learn that it takes more than 45 minutes to win a football match. We dominated the first half but that’s no good because at the end of it you come away, you’ve lost 2-0 and there's a completely different perspective on the game.”
Spurs: Glover, Walker-Peters, Ogilvie, Amos (c), Maghoma (Muscatt 24), Walkes, Edwards (Stylianides 75), Pritchard, Harrison, Miller, Oduwa (Tracey 75). Substitutes (not used): Goddard, McDermott (GK).
Everton: Hewelt, Jones (c), Robinson, Walsh, Feeney, Galloway, Henen, Davies, Evans (Duffus 61), Ledson (Charsley, 61), Dowell (Foulds 79). Substitutes (not used): Dyson, Gray (GK).
Goals: Everton - Henen 79, Foulds 85.
Yellow cards: Spurs - Amos 59; Everton - Davies 68, Foulds 82.
Referee: Steven Rushton.
Our first away game in Premier League 2 takes place in a week's time as we go to Reading's Hogwood Park training ground to face a Royals outfit which opened their 2016-17 campaign with a 2-0 victory away to Arsenal on Friday.