Rovers Under-18s booked their place in round four of the FA Youth Cup thanks to Georgie Gent's superb strike, but Mike Sheron's side were certainly made to work to progress by Carlisle United.
Gent's stunner put Rovers ahead on the 20-minute mark, and that proved to be the match-winning moment to ensure Sheron's youngsters booked their place in the next round.
Having bossed the first half possession, Rovers were forced back for the majority of the second, with good positioning seeing Lenni Cirino and then Ben Pleavin heading off their own line to keep Felix Goddard's clean sheet intact.
Goddard impressed on his cup debut for the club, producing one brilliant save midway through the second half to deny Elliot Day.
And although Rovers squeezed through, Sheron's side will know that they have to be better if they are to emulate last season's run that took the club to the semi-finals stage of the competition.
The hosts had the better of it inside the opening five minutes at Brunton Park, with Lewis Bell curling wide of Goddard's goal from the edge of the box.
United ventured forward again as they looked to capitalise on a fast start, with Dylan Garvey testing Goddard, before Rovers provided the sucker-punch up the other end when they went ahead through a terrific finish from Gent.
A quick counter attack saw a fine ball played through from captain Jared Harlock, and Gent was onto it in a flash before lashing past Isaac Robinson and into the top corner from a fairly acute angle.
The goal gave Rovers confidence, with Sheron's side beginning to boss both the possession and the chances against the Blues.
Playing with such freedom, Jay Haddow was up from defence and went close to doubling the visitors' advantage, but the right back's left-footed curler was headed away from danger by a home defender.
As it was, Rovers deservedly went into the break with a narrow advantage thanks to Gent's scorcher, but the home side came out fighting at the beginning of the second 45 minutes.
A fine free kick routine saw Goddard alert to tip over Elliot Day's from close range just six minutes after the interval, with United coming out looking for the equaliser.
Excellent covering from Cirino saw the left back in the right place at the right time to head off the line, with Max Kilsby's strike destined for the corner were it not for the Rovers left back just before the hour mark.
With ex-Rovers coach Eric Kinder in charge of the hosts, the Cumbrians continued to probe as the half progressed, with Sam Fishburn heading over from Lewis Bell's teasing cross from the left.
Rovers were being pushed back and Goddard's goal was living something of a charmed life as more fine defending from Rovers saw Ben Pleavin nod Day's header off the line with under 15 minutes of the third round encounter remaining.
In a rare foray forward, it looked as if Rovers secured their place in the next round with five minutes remaining when Gent headed home from close range, but the flag was up, the winger was denied his and Rovers' second, and the score remained slender.
Carlisle were never going to crash out of the competition without a fight, and Bell's free kick floated over the upright in what was the final chance of a game where the talk will be more about Rovers' defensive steel and resoluteness rather than their attacking play.
The result sees Rovers progress, with the draw for round four to be announced in due course.
Carlisle United Under-18s: Robinson, Steele (Taylor, 73), Kilsby, Leslie (c), Barnett, Day, Ellis (Watt, 63), Walton, Fishburn, Garvey (Rooks, 30), Bell.
Unused substitutes: Hill, Simons, Breeze.
Rovers Under-18s: Goddard, Haddow, Cirino, Pleavin, Garrett, Gamble, Wood (Chmiel, 67), Harlock (c), Gilsenan, Wharton (Weston, 76), Gent (Biniek, 90).
Unused substitutes: Blease, Pratt, Montgomery, Fyles.
Goal: Gent, 20.
Booked: Garrett, 56.
Referee: Chris Joyce.