Rovers side-stepped a potential FA Cup upset with few headaches to set up a second round clash with Paul Dickov’s former club Oldham Athletic.
A Curtis Main brace plus strikes from James Coppinger and Richie Wellens put Rovers into a commanding 4-0 win at Weston-Super-Mare.
But Liam Monelle pulled back a deserved consolation strike for the Conference South strugglers with the last kick of the game.
Rovers were in full control in the first half and carried a three-goal advantage into the break.
They eased off the gas after the break allowing Weston to have more of a say but there was never any real sign of a comeback.
After the original staging was postponed by referee Tim Robinson at the 11th hour, Rovers wasted no time in getting the job started in dealing with the Conference South strugglers.
Main gave them the lead just 15 minutes in after a period when Rovers totally dominated possession.
A short corner was played to Kyle Bennett who skipped past a challenge and drilled a shot with Main getting a touch to send the ball past the impressive Purnell.
Main then doubled the advantage on 33 minutes. Good work from Coppinger on the right saw him find space for a shot which was blocked only for Main to nip in and turn home.
And with half time moments away Coppinger made it three. Excellent work from Richie Wellens undid the Weston defence with Coppinger producing a stunning strike to beat Purnell.
The gap could have been wider had Rovers not seen two efforts ruled out in the early stages.
An impeccable observed minute’s silence preceeded the game in memory of the five teenagers killed in a horrific crash in Doncaster at the weekend.
Paul Keegan thought he had put Rovers ahead on two minutes, scrambling the ball home after a Coppinger corner, but Robinson blew for a foul.
And Main was also denied the opener on eight minutes when he drilled home a Coppinger cross but was judged offside.
Main really should have done better on 12 minutes when played in by Wellens but sent his shot harmlessly wide of the near post.
And Keegan really ought to have doubled the lead on 18 minutes when through on goal but sent a tame effort straight at Purnell.
Weston grew into the game and had their first real effort on goal after 22 minutes when Joe McClennan found space but drilled wide from the edge of the box.
A fantastic save from Purnell denied Rovers a second on 28 minutes. The Weston keeper turned away a header from Robinson.
It was the post that denied Rovers a minute later. Reece Wabara sent in a cross, Main dummied and Coppinger scuffed a shot which came back off the upright.
Weston saw plenty of the ball for the first time in the game but were hit with a suckerpunch on 63 minutes as Rovers broke.
Kyle Bennett surged up field, cut inside and slid in a pass to Wellens who finished well.
Weston continued to have more of a say than their first half efforts but it was still Rovers who unsurprisingly looked the more threatening.
Enda Stevens played a low pass in for Curtis Main but Weston keeper Luke Purnell saved well.
Main was involved again on 73 minutes after being played in by Bennett but his first time shot was well over.
Purnell saved his best save for late in the game. A fine pass from substitute Marc De Val found another in Harry Forrester but his strike was saved well by Purnell.
Theo Robinson really should have made it five with five minutes to go as he brought the ball down in space but fired well over the bar.
But it was Weston who would have the final say in goalscoring terms.
Dayle Grubb’s cross caused havoc in the Rovers box and Monelle popped up to poke home the consolation.
Rovers: Johnstone, Wabara, McCullough, Butler, Stevens, Coppinger (Forrester 68), Wellens, Keegan (De Val 71), Bennett (Whitehouse 79), Main, Robinson.
Subs not used: Marosi, Wakefield, Middleton, Tyson.
Weston: Purnell; Brown, Barnes, Jordan, Fortune, McClennan (Teale 80), Mawford, Cane, Ash (Monelle 71), Grubb, Bath (Harris 71).
Subs not used: Llewellyn, Fiddes, Camper, Jackson.
Referee: Tim Robinson (West Sussex)
Paul Dickov named a strong side to face Conference South outfit Weston-Super-Mare in the rearranged tie.
Luke McCullough and Andy Butler returned at centre half as part of four changes to the side that lost against Sheffield United at the weekend.
Loanee Butler was ineligible to play against his parent club while McCullough failed to return from international duty with Northern Ireland in time to feature.
Theo Robinson and Kyle Bennett also came into the side as part of four changes made by Dickov.
Liam Wakefield, Nathan Tyson and Harry Forrester dropped to the bench while Jamie McCombe missing out entirely after having an injection in his back.
Weston-Super-Mare made three changes to the side that lost 1-0 to Havant and Waterlooville at the weekend.
In came Aaron Brown, Oliver Barnes and Jacob Crane with Sam Teale, Jake Llewellyn and Jamie Edge all missing out.
The referee for the match was Tim Robinson, the same man who called the original game off just 20 minutes before kick off.