Ash Taylor's first half strike booked Tranmere's place in the Johnstone's Paint Trophy northern quarter finals.
The defender scored the only goal of the game at the Crown Ground to set up an away tie at Chesterfield.
It was a fitting strike for Taylor found the target for Tranmere in the abandoned fixture eight days earlier to briefly become the Club's leading scorer for the season only to have his effort erased from the record books.
Otherwise, it was a fairly even game with Accrington hitting the woodwork while Tranmere had several decent chances to add to their tally.
There was just one change to the team that started the abandoned match at the Crown Ground eight days earlier, with John Welsh returning from suspension to take the place of Robbie Weir in midfield. Adam McGurk and Enoch Showunmi were named among the substitutes with Dave Raven and Weir, as Michael Kay, Zoumana Bakayogo and Mustafa Tiryaki rejoined the starting line-up. Former Rovers midfielder Charlie Barnett missed out for Stanley through injury.
A surging run from left back from Bakayogo started the first attack of the game on four minutes , but after the ball reached David Buchanan on the left side of the Stanley area, his cross went just over the head of Lucas Akins at the far post.
Owain Fon Williams had to claw a deflected Danny Coid effort away from goal while in a quick counter attack Stanley's Ian Dunbavin had to race out of his area to clear the ball from the path of Jose Baxter.
Ian Craney fired high over the bar after winning the ball in the middle of the Tranmere half on 13 minutes and at the other end a long range effort from Buchanan had to be blocked by Dean Winnard just in front of goal.
Kurtis Guthrie could have opened the scoring for the hosts on 18 minutes when he jumped highest to meet a cross from the left but his header went high over Fon Williams' bar.
A shot from Ian Goodison was blocked after penalty appeals were turned down when Akins went down inside the area after cutting inside from the right, while Bakayogo raced clear on 28 minutes after a quick throw from Fon Williams and saw his low shot saved by Dunbavin.
A wonderful cross field pass from Baxter released Akins on 29 minutes and the former Huddersfield striker played the ball across the area to Tiryaki who looked set to open his Rovers account only for Kevin Long to slide in and block his effort.
Rovers survived a prolonged goalmouth scramble on 33 minutes as Stanley moved the ball around following a corner but couldn't quite work the shooting angle they were looking for.
Bakayogo needed a spell of treatment in the changing rooms after a clash of heads deep in the Stanley half on 36 minutes and while the defender was off the pitch Rovers took the lead. A free kick was sent into the Stanley area and after Baxter's attempt was blocked the rebound fell to Ash Taylor who rifled his shot into the net.
As play restarted Bakayogo was replaced by McGurk, with Buchanan taking up his usual left back role in place of the Frenchman.
An underhit back pass from Kay gave Guthrie possession inside the Rovers area on 43 minutes but the visitors' momentum was broken up by Welsh and Tranmere quickly started an attack of their own, while Padraig Amond fired just past the post soon after.
The final chance of the half saw Baxter slide in on a challenge with Dunbavin outside the area and the ball flew high in the ball and landed just wide of an empty net.
Guthrie sent a right foot shot wide of the target from 20 yards in the third minute of the second half and an attack from Andrew Procter was brought to an end by Taylor soon after.
The early stages of the second half were scrappy with neither team able to create a clear opening as possession was wasted at both ends of the pitch.
On 65 minutes Goodison brought a save out of Dunbavin with a back post header from Labadie's free kick and a few minutes later Akins headed over the bar from close range. It was Akins' last involvement with Robbie Weir coming on in his place soon after.
Guthrie sent a header narrowly past Fon Williams' right hand post on 70 minutes as Stanley searched for an equaliser and the striker brought a save out of the Rovers keeper two minutes later with a low effort from distance.
A 25 yard shot from Labadie went just past Dunbavin's goal after the midfielder picked up a loose ball in the centre circle and McGurk put an angled left foot shot past the right hand post when one on one moments later.
A remarkable goalmouth scramble on 81 minutes from Ian Craney's chipped free kick saw Stanley hit both the post and the bar and have two headers cleared off the line by Goodison and Buchanan as Rovers threw everything in the way to hold on to their lead.
Craig Lindfield fired just wide of the Tranmere goal from outside the area with six minutes remaining while McGurk's cross at the other end went beyond Tiryaki.
With Dunbavin out of his goal McGurk put his long range effort over the bar from wide on the left on 89 minutes, the last real chance of the game for either side.
Accrington Stanley: Dunbavin, Coid (Lindfield 68), Winnard, Procter, Guthrie, Craney, Joyce, Murphy, McIntyre, Long, Amond (Fletcher 87). Unused Substitutes: Murdoch, Burton, Taylor.
Tranmere: Fon Williams, Kay, Taylor, Goodison, Bakayogo (McGurk 40), Akins (Weir 69), Welsh, Labadie, Buchanan, Baxter, Tiryaki. Unused Substitutes: Coughlin, Raven, Showunmi.
Referee: James Adcock
Yellow cards: Labadie (45+3), Tiryaki (50), Winnard (63), Kay (90+3)
Follow Tranmere on Twitter at www.twitter.com/tranmererovers.