A win would leave Allan Johnston’s side, who beat Peterhead 3-0 in their first match, needing only a point from their final game at home against Stirling Albion to seal their place in the last 16.
The East End Park boss is looking for the same level of performance which earned that 1-0 success at Dens Park.
Johnston said: “We showed a lot of quality in that performance. We created lots of chances and restricted Dundee to very little. The games are coming along really quickly but we cannot let our pace drop.”
Brechin manager Darren Dods, meanwhile, is hoping the boost from a 2-1 victory at Stirling – City’s first since a Scottish Cup win over Buckie Thistle last November – will help against the Pars
Dods said: “We have a bit more confidence after beating Stirling last week.
“That will be needed as Dunfermline did really well at Dundee, where they displayed a very solid defensive line, a lot of energy in midfield and very good forward play.”
Dundee’s hopes of bouncing back quickly have taken a knock as they are without six players for their match away at Peterhead.
Nathan Ralph, Genseric Kusinga, Darren O’Dea, Glen Kamara, Roarie Deacon and Sofian Moussa are all out injured, but whatever side manager Neil McCann puts out will be expected to perform better than the one he chose at the weekend.
He said: “Our application was not what it should have been and the boys know I was not happy. We have quality in our squad and I am looking for that to be prevalent in this game.”
Peterhead manager Jim McInally wants his side to display the vim and vigour that was missing during Saturday’s 2-0 defeat by Stirling Albion.
McInally said: “Our energy levels need to be higher as Dundee have a point to prove. They also need a win and goals to be in the qualification hunt.”
A win at Arbroath would see Ross County top Group A.
Co-manager Stuart Kettlewell said: “We have won two games and not conceded so it has been a good start. Arbroath will make it difficult, however, I want us to keep things going positively.”
Arbroath manager Dick Campbell is determined that the Gayfield men give their slim hopes of qualifying for the knockout stage a boost. He said: “It is a long shot but we will look to move to the eight-point mark. That may just get us through in second place.”
In Group B, Montrose make the short trip to Angus rivals Forfar Athletic looking to stay in the hunt for a place in the knockout phase.
Wins over Falkirk and East Fife have given the Links Park side an opportunity that manager Stewart Petrie was not expecting. He said: “Getting through was not a target that was set. We were looking to be prepared for League 1 and anything more is a bonus.
“We will look to recover from losing to St Johnstone on Saturday and then see what the weekend’s results bring us.”