The Toffees' stars of tomorrow deserved the win on the night, creating the better chances, but had to wait until the 91st minute of an entertaining game before Youseff Chermiti beat Scott Flinders from the spot from a contentious penalty award.
But the biggest post-match talking point was a possible injury problem for Stephen McLaughlin, making his first start of the campaign after injury and going off after needing treatment for a tight groin soon after half-time.
Young centre half George Cooper again showed quality at the back for a largely second string home side, but hopes that tonight could provide much-needed goals for James Gale and Will Swan were dashed by some fine Everton defending.
After hurtful exits from the Carabao Cup and FA Cup over the past week, this one will quickly be forgotten as Mansfield now begin to focus on Saturday's important League Two game at Salford City.
Not surprisingly Mansfield made nine changes for the game with only Callum Johnson, and Bailey Cargill still in from the weekend starting XI.
George Cooper and George Williams began in central defence with Cargill ahead of them in the holding role, looking very comfortable in the position, and McLaughlin also impressing in a midfield role before his injury.
Everton included veteran club skipper and Ireland captain Seamus Coleman as he continued his comeback from a serious knee injury at the end of last season.
There were also minutes for other Toffees players with first team experience like Joao Virginia, Lewis Dobbin, who had a good loan spell with Derby County, and Youssef Chermiti.
Stags started well and won a fifth minute corner which saw a scramble and Johnson poke the ball across the face of goal.
On seven minutes Everton showed for the first time as Dobbin raced down the middle but fired straight to Flinders.
A minute later more room was afforded to Dobbin and this time he shot over.
An Everton break into the home box on 17 minutes saw a scramble that ended with Johnson clearing.
Stags resumed the offensive and both Abdullah and Boateng had good efforts blocked.
On the half-hour Chermiti headed over at the near post from a left wing cross and three minutes later McLaughlin was narrowly wide wit an excellent free kick from a central position 30 yards out.
A minute later Abdullah curled one just over from the right hand side of the box.
In the 42nd minute Stags conceded a central free kick 25 yards out but Hunt sent his effort straight into the home wall and a minute later Flinders saved a low shot from Chermiti with Cooper sliding in superbly to mop up the loose ball and clear before Chermiti could try a follow-up.
As half-time neared the home side forced three successive corners but could not force the ball home as an enterprising half by both teams ended scoreless with only routine saves to be made.
McLaughlin had been excellent on his return from injury but, worryingly, on 49 minutes went down after having a shot blocked and required treatment before going off to be replaced by Maris.
Cooper got a brave block in on a Chermiti shot at the near post on 54 minutes that conceded a corner from which Okoronkwo nodded over.
On 59 minutes we saw the first real save of the game as Hunt went down the middle and forced Flinders down full length to his right to stop.
On 63 minutes Flinders made an even better stop with a superb one-handed block after Dobbin had caught the ball perfectly on the half-volley with a powerful snapshot.
Djankpata was too high with the Toffees' next effort as the visitors enjoyed a good spell and on 65 minutes Dobbin cut in from the left and saw his finish bounce over off the top of the crossbar.
In reply Swan had a tame shot blocked for a corner from which Gale glanced a header wide.
Mansfield gave away another free kick 20 yards out just left of centre and this time Metcalfe curled narrowly over the top with a fine effort.
John's foul on Cargill on 70 minutes saw the gane's first yellow card produced.
Virginia was then safely behind a curling free kick by Boateng from the by-line that he curled in wickedly.
Then Johnson drilled a low ball into the box which Swan turned tamely at the keeper.
Chermiti went in late on Williams on 73 minutes to be added to the book before Stags made four changes.
After McAllister pulled a low shot wide for Everton, Stags came very close on 79 minutes as Bowery drilled in a low left wing cross. Gale's finish was half-blocked by the challenge of Astley and the ball span just wide of keeper and post.
Everton should have grabbed the lead on 84 minutes after a lightning break down the right by Dixon. He pulled an inviting low pass back into the path of Barker who, with the goal at his mercy, fired well over.
The deadlock was finally broken in the first of five added minutes from the penalty spot.
The referee decided Chermiti was pulled back by Cooper as he turned in the box and he pointed to the spot to Mansfield’s anger. But the Portuguese star stepped up and smashed his kick home straight down the centre.
On 93 minutes Stags youngster Flanagan tried his luck from the edge of the box and forced a good save out of Virginia as Everton hung on for a first group win.
STAGS: Flinders, Johnson (Flint 73), McLaughlin (Maris 51), Cargill (Flanagan 73), Macdonald (Bowery 73), Gale, Cooper, Williams, Swan, Abdullah (Brunt 73), Boateng. SUBS NOT USED: Pym, Taylor.
EVERTON U21: Virginia, Coleman (Dixon 66), Chermiti, Astley, John (Barker 73, Heath 90), Hunt, Dobbin, Campbell, Djankpata (McAllister 66), Metcalfe, Okoronkwo. SUBS NOT USED: Barrett, Butler, Sherif.
REFEREE: Neil Hair.
ATTENDANCE: 819 (74 away).