Demarai Gray's second goal in three days confirmed Everton's place in the Carabao Cup third round as the Blues secured a 1-0 win over Fleetwood Town at Highbury Stadium.
The Toffees produced a controlled performance against their League One opponents on a memorable night for First-Team debutants Lewis Warrington and Stanley Mills.
Everton will discover who they face in the third round of the competition on Wednesday evening.
Manager Frank Lampard made seven changes from the side that started against Nottingham Forest in the Premier League at the weekend, with Asmir Begovic, Michael Keane, Seamus Coleman, Reece Welch all handed their first minutes of the season.
Summer signings Rúben Vinagre and Amadou Onana, meanwhile, made their maiden starts for the Club.
The Blues boss was forced into making a late switch, too, with Tom Davies dropping out in the warm-up to be replaced by eventual match-winner Gray.
Everton started brightly, enjoying plenty of possession in the opening exchanges, while Fleetwood focused on remaining organised and stubborn in defence.
The first sight of goal was fashioned just after the quarter-hour mark, when Alex Iwobi - instrumental throughout in the heart of midfield - slid a pass into the penalty area for Vinagre. Unfortunately, the wing-back's chipped cross was inches out of Salomon Rondon's reach.
While much-changed, Lampard opted to remain consistent with his 3-4-3 system from the start and the Toffees looked to stretch the pitch by utilising their wing-backs throughout the opening period.
It nearly paid dividends when Welch - making his first senior start - played the ball into Onana and the Belgian subsequently picked out Nathan Patterson with a perfectly-weighted 50-yard pass.
Patterson controlled instantly before nicking the ball past his marker and finding McNeil with a low cross, but the shot was miscued off target.
Everton deservedly broke the deadlock on 28 minutes, when McNeil seized on a loose pass in the Fleetwood defence before finding Iwobi on the edge of the penalty area.
The Nigeria international coolly picked out a slide-rule pass to Gray, who made no mistake with a curling finish into the far corner of the net.
Everton kept their hosts at bay for the majority of the first half but Scott Brown's side did threaten in stoppage time, as Cian Hayes burst down the right channel before cutting in-field and stinging the palms of Asmir Begovic with a venomous left-footed strike.
In a second half void of clear-cut chances, the Blues controlled proceedings.
Everton's best chance arguably came when Rondon won possession on the halfway line before leading a three-versus-three counter-attack, however, his eventual pass for Iwobi was slightly over-hit, allowing Fleetwood defender Drew Baker to recover and snuff out the danger.
Boyhood Evertonian Warrington was introduced just after the hour for his First-Team debut, as Lampard shuffled his pack and switched to a 4-3-3 shape.
Mills, who signed a new three-year deal less than a fortnight ago, then became Everton's latest Academy graduate, replacing goalscorer Gray with 15 minutes remaining.
Everton's attention now reverts back to the Premier League, with a visit to Brentford's Gtech Community Stadium on Saturday (3pm BST kick-off).
