Callum Dolan came off the bench to send Rovers through to the second round of the FA Youth Cup, courtesy of a 1-0 victory over Tranmere.
After a goalless first half, in which Rovers striker Dan Butterworth missed an open goal, Dolan headed home the only goal of the game just past the hour mark.
It was nothing more than Rovers deserved, having dominated the game for long spells, but a combination of wayward finishing and inspired goalkeeping from Tranmere's Patrick Wharton kept the contest alive.
Rovers' reward is a home tie against Wrexham in the second round.
The game started at a lively pace, with both sides exchanging shots in the early stages.
The first chance of the game went Rovers' way on eight minutes, as Butterworth slipped the ball through to Callum Wright, but the Tranmere keeper came rushing out to make a smothering save.
At the other end, James Devine and James Salkeld both failed to test Matthew Campbell with efforts from the edge of the area, before Rovers were twice off target, as Brad Lynch blazed over the bar and Butterworth's hooked effort, from Jack Vale's cross, just cleared the upright.
Vale delivered another dangerous cross on 17 minutes, but the unmarked Lynch couldn't convert at the far post.
Rovers threatened again at the midway point in the half, as Wright played the ball into the path of Lynch, who skipped past a couple of challenges, before forcing a smart diving save from Wharton.
The hosts went close to breaking the deadlock moments later, as Ali Al-Hamadi advanced towards the edge of the Rovers area, before looking to pick out the bottom corner, but Campbell made a fine save low to his left.
Rovers ought to have opened the scoring on 34 minutes. Butterworth beat the offside trap to latch onto a ball over the top, he then rounded the keeper, but with an open goal to aim at, his shot struck the outside of the post.
On the stroke of half-time, Al-Hamadi tried his luck from a long way out, but Campbell got his body behind it, then Lynch again blazed over the bar from Andy Jackson's deep cross.
Rovers started the second half strongly, creating some decent chances in the opening exchanges.
On 48 minutes, Vale twisted and turned his marker in the area to create space for a shot, which Wharton saved well.
Moments later, Butterworth showed quick feet to beat his man, before seeing his low shot saved. Then, Vale's crisp strike from the edge of the box stung the palms of Wharton, who did well to tip the ball over the bar.
In need of a spark, Rovers introduced Dolan on 55 minutes and the substitute made an instant impact.
Less than seven minutes later, Jackson swung over a cross from the right and Dolan got up well in the middle to head the ball into the top right corner.
It should have been 2-0 two minutes later, as Lynch slipped the ball through to Butterworth, who dragged his shot just wide of the far post, when a return pass was possibly the better option.
Tranmere made three changes as they looked for a way back into the game, but it was Rovers who looked the more likely of adding a second.
On 80 minutes, Doloan had the ball in the back of the Tranmere net for a second time, but it was ruled out by the linesman's flag.
Kyle Connell was then introduced for Lynch and the substitute was immediately involved, racing through on goal, but he fired inches over the bar.
Trailing by just a solitary goal, Tranmere always remained in contention and their big chance arrived three minutes from time.
Substitute Jake Burton found himself clean through on goal, but Campbell came out to make a crucial save and Burton couldn't convert the rebound.
Butterworth then fired inches wide of the bottom corner at the other end, as Rovers safely made it through to round two.
TRANMERE: Wharton, Solomon-Davies, Ellison, Devine, Long, Drysdale, Salkeld (Burton 68), Moreton (Spellman 78), Thompson (Brett 68), Al-Hamadi, Walker-Rice.
Subs not used: Passant, Kerr.
ROVERS: Campbell, Jackson, Paton, Buckley, Carter, Barnes, Vale, Wilson (Dolan 55), Butterworth, Lynch (Connell 80), Wright.
Subs not used: Winterbottom, Chan, Pike.
Goal: Dolan (62)