Rovers secured a safe passage into the semi-finals of the Lancashire Senior Cup but it wasn't easy against a resolute Everton side.
First half goals from Joe Rankin-Costello, Jacob Davenport, Harry Chapman and John Buckley put Rovers in command going into the interval in crisp conditions.
But any hopes of a comfortable second half were eradicated just before the hour when Rhys Hughes forced a goal back before Kieran Phillips added a second of the afternoon with seven minutes remaining.
Hughes' second and his team's third made sure of a nervy ending at Brockhall Village, but Rovers kept them at bay to book their place in the next round.
Everton started well, with Hughes testing ex-Everton trainee Joe Hilton early on, with the Rovers ‘keeper forced to tip over the midfielder’s dipping free kick inside the opening minute of the encounter.
At the other end, Danny Graham lashed wide after getting on the end of a poor header by visiting defender Reece Welch.
It was an intense start from Rovers, with Davenport and Rankin-Costello firing wide in a lively starting 10 minutes of the cup clash.
Billy Barr’s youngsters did finally get the goal their dominance deserved just before the half hour mark. Good work from Harry Chapman saw him cut inside from the left and tee up Rankin-Costello, who made no mistake with a calm, first time finish.
It was 2-0 just a moment later and once again it came from Rovers’ left-hand side. This time it was Lewis Thompson who ventured forward, with Davenport lurking at the back post to pounce and slot beyond Nico Hansen and double the advantage.
Rovers really upped the gears and it was Chapman who got his name on the scoresheet just a few minutes later. A neat one-two between the scorer and Danny Graham saw the winger get on the end of the striker’s flick and bend a lovely finish low into Hansen’s left-hand corner.
There was time for a fourth and it came from John Buckley, who slalomed away from a number of challenges before finding a way into the box and slotting home on the stroke of half time.
Rovers continued to boss the game, but it was the visitors who got the next goal of the game through Hughes. He ventured forward and caught Hilton out with a strike from 20 yards that nestled nicely into the bottom right-hand corner.
The Toffees gained confidence from the strike, and Manasse Mampala forced Hilton to hold a long range effort as they pressed to really get back into the game.
Only a strong hand from Hansen denied substitute Ben Paton from slamming home after a Graham knockdown, with Barr’s boys looking to regain their three-goal advantage straight away.
A terrific attempt from Rankin-Costello went closer still for Rovers, with the midfielder beating Hansen but not the upright, with his lobbed effort clipping the top of the crossbar.
Kieran Phillips nearly reduced the score further later on, but he slid wide after being played in by half time substitute Seb Quirk.
But with his next chance he made no mistake, slotting low past Hilton with seven minutes remaining after being fed by Lewis Warrington.
The crossbar was Rankin-Costello’s enemy again just seconds later, with the woodwork being in his way again after he nonchalantly looped a strike over Hansen again, before the danger was cleared.
It proved to be a nervy ending to the game for Rovers when Hughes found the net again from the edge of the box that Hilton would have been disappointed with after getting a touch on the strike in the final minute of normal time.
But in the end Rovers held out despite the visitors thowing everyone forward late on, to book their place in the next round of the competition.
Rovers Under-23s: Hilton, Sobowale, Thompson, Davenport, Carter (Whitehall, 59), Barnes, Rankin-Costello, Smallwood, Buckley, Graham (c), Chapman (Paton, 44).
Unused substitutes: Eastham, Mols, White.
Goals: Rankin-Costello, 27, Davenport, 29, Chapman, 33, Buckley, 45
Booked: Thompson, 15
Everton Under-23s: Hansen, Hosie, Anderson (Lowey, 51), Hughes, Higgins (Quirk, 46), Iversen (c), Phillips, Carroll (Warrington, 46), Mampala.
Unused substitutes: Barrett, Warrington, Cannon,.
Goals: Hughes, 58, 90, Phillips, 83
Booked: Carroll, 22, Higgins, 25, Hosie, 41
Referee: Richard Aspinall.