Josh Bowler's first half strike proved to be the match-winning moment as Rovers' journey in the Premier League Cup came to an end.
Bassala Sambou's spot-kick handed the hosts the early advantage, before Bowler's curler doubled Everton's lead before half time.
Damien Johnson's side largely dominated the second half and pulled a goal back midway through it thanks to Harry Chapman's fine solo effort.
The opportunities came and went for the visitors, with Chapman testing home goalkeeper Joao Virginia on a couple of accastions, but it was the Toffees who booked their place in the semi-finals of the competition, sending Rovers out.
The likes of Chapman, Joe Nuttall, Dan Butterworth, John Buckley and Jacob Davenport all started at Goodison Park, with Johnson armed with Jack Vale on the bench if needed.
But a poor start saw Rovers go behind after only three minutes, as a penalty was awarded to the hosts.
When Doyle's stray first touch allowed Anthony Gordon to nick the ball off him, and in attempting to recover, Doyle brought down the winger in the box to hand Everton an opportunity from the spot.
Up stepped Sambou, who confidently sent Charlie Albinson the wrong way and give the Premier League 2 Division 1 champions the lead.
Soon after and quick wing play from Bowler saw the midfielder cut in on his left foot, but Albinson was there to turn the attempt behind for a corner.
At the other end, Davenport fired just wide in a lively opening 15 minutes at a chilly Goodison.
Rovers were struggling to find a way through a resolute Everton defence, with the hosts going close to doubling their tally before the half hour mark when Nathan Broadhead's 20-yard strike curled just past the post.
But a moment later it was 2-0. Bowler showed some neat touches to work a yard before curling a superb effort beyond the dive of Albinson and into the right-hand corner from the edge of the box.
Albinson did well to keep the score as it was a couple of minutes later, reacting well to flick away a close range Morgan Feeney header after Broadhead's outswinging corner ended up falling to the Toffees captain.
Following a slow start to the second half, Chapman gave Rovers hope of a comeback just after the hour mark.
The winger skipped past the challenge of Ryan Astley before slotting a low effort from an acute angle under Virginia and into the back of the net to halve the deficit.
Rovers' tails were up at this point and after another solo run from Chapman saw him slip at the vital moment, Virginia was out smartly to deny Nuttall just a few moments later.
With time running out, Chapman's inswinging corner was nodded just over by substitute Vale, who had earlier entered the action in place of Nuttall.
Chapman was causing problems and another darting run forced another opportunity, but Virginia was there with a strong hand to stop the winger from forcing an equaliser with only one minute remaining.
And that was to be that for Johnson's youngsters, whose Premier League Cup run came to an end at the quarter-finals stage, despite bossing the second half.
Everton U23s: Virginia, Astley, Foulds, Markelo, Feeney (c), Gibson, Bowler (Denny, 89), Adeniran, Sambou, Broadhead (Hornby, 66), Gordon (Mampala, 76).
Unused substitutes: Hilton, Ouzounidis.
Goals: Sambou pen, 4, Bowler, 27
Booked: Foulds, 44, Gordon, 48, Feeney, 51, Bowler, 87
Rovers U23s: Albinson, C. Doyle, Thompson, Davenport, Magloire, Carter (Mols, 60), Rankin-Costello, Buckley, Nuttall (Vale, 76), Butterworth, Chapman.
Unused substitutes: Eastham, Annesley, Whitehall.
Goal: Chapman, 64
Booked: Magloire, 63
Referee: David Richardson.