The home side finished last in 10th place of the Scottish Championship with 23 points and were relegated to League One, while the visitors finished the overall top-flight season in sixth with 42 points.
Match preview
The hosts are the only side in their five-team League Cup group to have not played a game yet, and are currently third.
Arbroath will have been immensely disappointed with their showing in the 2023-24 season as they were relegated to League One.
Having scored 35 goals and conceded 89, they were the division's worst offensive and defensive team.
Considering they finished second in the Championship as recently as the 2021-22 campaign, the fact that they have been demoted to the third tier of Scottish football will be of huge concern to manager Jim McIntyre.
McIntyre has been in charge since December 2023 after replacing Dick Campbell, whose last game at Gayfield saw his side lose 2-1 against League Two Spartans in November in the Scottish Cup.
Arbroath come into the game in poor form having lost their two pre-season friendlies, and prior to the end of the 2023-24 season they lost 10 straight Championship matches.
McIntyre's side have also struggled at Gayfield Park having lost 10 of their last 14 competitive home fixtures.
Interestingly, one of Arbroath's friendly losses was against Tuesday's opponents, with Dundee winning 3-1 on June 29.
The visitors come into the game top of their League Cup group having won 7-1 in their opening match against Bonnyrigg Rose on Saturday.
Curtis Main performed exceptionally well, and left with the match ball after scoring a hat-trick.
Manager Tony Docherty has been in charge of Dundee since May 2023, and has an overall record of 13 wins, 12 draws and 18 losses.
Under his leadership last term in the top flight, his team scored 44 goals and conceded 54 times in the regular season, and after 33 games this made them the division's joint fifth best offensive and 10th best defensive side.
Docherty's side also began their last League Cup campaign with a victory against Bonnyrigg Rose, but considering they only won 1-0, it is fair to say that they have made a much more impressive start to the current season.
Dundee Scottish League Cup form:
W
Dundee form (all competitions):
Team News
The hosts will want to hand several of their summer signings a first competitive appearance, so expect the likes of goalkeeper Robbie Hemfrey and centre-back Jack Wilkie to play.
In midfield, it would not be a surprise to see Liam Callaghan start, while new forwards Gavin Reilly and Calum Gallagher may have to battle for a starting spot.
As for the visitors, Curtis Main and Lyall Cameron are almost certain to start given the pair scored three and two goals respectively against Bonnyrigg Rose on Saturday.
Elsewhere, it would be surprising if manager Docherty made many changes, so defenders Ryan Astley and Juan Portales, who both scored against Bonnyrigg Rose, could be in line for further starts.
Arbroath possible starting lineup:
Hemfrey; Walker, Wilkie, O'Brien, Steele; Callaghan, Slater; Dow, Gold, Murray; Reilly
Dundee possible starting lineup:
McCracken; Portales, Robertson, Astley; Ingram, McGhee, Sylla, Cameron, McCowan; Tiffoney, Main
We say: Arbroath 1-4 Dundee
Considering that Dundee managed to win 7-1 last time out, it is fair to say that they will be confident of securing another victory.