The game is Tranmere's final in the group and leaves them on four points after one win, one draw and a defeat, and depending on results elsewhere, they could still progress to the next round of the competition.
Rovers were able to field a much stronger side than recent weeks, as Calvin Zola, Mike Jones and Craig Curran all started for Rovers, with Shaun Garnett allowed to pick the first-teamers thanks to the return to fitness of Chris Greenacre and good form of Gareth Taylor. Elsewhere, Louis Corrigan and Ryan Mitchell made their first appearances for the reserves on the left of midfield and in central defence.
Early signs of what the first half was to bring came early on as Craig Curran headed Mike Jones' cross narrowly wide after the Tranmere winger had made an excellent run down the right.
Tranmere opened the scoring soon after however thanks to defender Ashton Taylor. A dubious free-kick was awarded after Curran went down near the corner flag for Rovers. Cresswell put the set-piece in, and with the ball having dip and curl on it, it fell for Ashton Taylor who vollied the ball home from the edge of the six-yard box.
Chester didn't look able to handle the Tranmere front two of Curran and Zola and before long Rovers had got a second, with the pair combining upfront.
Zola nodded on a long ball to Curran who ran free of the defence towards the area and after passing just inside the 18-yard box, with the defenders quickly catching up with him, the young prodigy netted under former Rovers 'keeper Phil Palethorpe and found the back of the net.
Tranmere could have had a third soon after as Aaron Cresswell curled a free-kick over the wall but saw it saved by Palethorpe after Curran had been brought down on the edge of the area.
Minutes later, the net again could have been bulging after Cresswell put a wonderful ball across the six-yard box and after a Chester player had almost diverted the ball into his own net, play was stopped by the waving flag of the assistant-referee for offside.
On 35-minutes, Tranmere defender Danny Holmes limped off and was replaced by Luke Denson at right-back whilst there was little else action in the remainder of the half with McWeeney having very little to do in the Tranmere goal.
The closest Chester came was with a shot from just outside the area which was powerfully hit straight at McWeeney on the half-volley after a quick break from City whilst another effort from inside the penalty area embarassingly crossed the goal-line somewhere near the corner flag.
The second-half saw little event too, as Rovers looked to both defend and extend their lead whilst Chester, themselves on one point in Group One before kick-off but having played a game less, looked to get back in the game.
One meaningful effort saw Palethorpe pull off an excellent diving save to stop Jones' free-kick whilst on 61-minutes, Calvin Zola, who had shown good strength and pace in the game with his best action came inside the centre-circle on half time as the striker brought the ball down brilliantly with his first touch and then spread the play wide to Mike Jones on the right whilst turning, was pulled off and replaced by Terry Gornell, presumably with Saturday's first team match at Swindon in mind.
After Zola's withdrawal, Rovers seemed to lose most of their impitus going forward as they had knowbody to hold the ball up when it got to the two front men, resulting in the defence seeing a lot more of the ball.
One man still on his toes however was winger Mike Jones, who appeared to be a class above the other 21 players on the pitch, getting forward well and turning the Chester defenders inside out on the right.
Rovers best chance of the half indeed was started by Jones, who crossed from the right. This was flicked on by Curran to Beahon who in turn passed across the 18-yard line to Gornell who, after controlling the ball, shot straight at Palethorpe.
Despite having posed no real previous threat to the Tranmere defence, Chester got back in the game on 85-minutes. The Deva Stadium side were awarded a free-kick about 25-yards from goal. Kevin Sandworth took the set-piece and sent the ball dipping over the wall. McWeeney dived on what appeared to be a regulation save, but somehow he rolled over the ball as it crept into the net.
Tranmere survived the remaining few minutes though as they hung on to claim a valuable win in the cup as they look to progress to the next round.
As far as players are concerned, Jones, Zola and Curran, as one would expect with them being first teamers, all impressed whilst Paul Henry put in one of his best displays of the season in midfield. Cresswell was, as always, impressive in defence, as was Ashton Taylor whilst debutant Ryan Mitchell had a good game in the heart of the Rovers back four.