The visitors, meanwhile, head into the midweek contest in fine form as they look to secure a fifth consecutive win.
Match preview
Dundee United have endured a difficult start to the season after beginning the campaign with an eight-game winless run that yielded only two points.
Liam Fox was appointed caretaker boss in August following the sacking of Jack Ross, and even though he was named as the club's permanent manager last month, a victory was proving to be elusive.
Fortunately for Fox and Dundee United, they finally claimed their first win of the season against Aberdeen at the weekend, and they achieved the feat in some style.
Aziz Behich, Tony Watt and Jamie McGrath all grabbed a goal apiece before a Ross McCrorie own goal wrapped up a memorable 4-0 victory for the Terrors.
With three precious points under their belt, Dundee United will now set about claiming a second straight win, which would move them off the foot of the Scottish Premiership table.
Hibernian began the campaign with one win from their opening five games, but since losing to St Mirren at the end of August, Lee Johnson's side have been unbeatable.
They will have the chance on Tuesday to claim a fifth consecutive victory after they extended their winning run at the weekend.
Ryan Porteous scored what proved to be the winner in Saturday's home meeting with Motherwell, ensuring Hibernian are now unbeaten in their previous 11 home league games.
The 1-0 victory also highlighted Hibernian's defensive resilience as they recorded their third clean sheet in four games.
As they turn their attention to Tuesday's away trip, the third-place side will be confident of claiming all three points after winning their last three away meetings with Dundee United in the Scottish Premiership.
Dundee United Scottish Premiership form:
L
L
D
L
L
W
Dundee United form (all competitions):
L
W
D
L
L
W
Hibernian Scottish Premiership form:
D
L
W
W
W
W
Team News
Steven Fletcher and Charlie Mulgrew are doubts for Tuesday's contest after missing the win over Aberdeen due to injury issues.
Peter Pawlett will be on the bench again after returning from injury to appear as a late substitute on Saturday.
McGrath and Watt are set to retain their places in the frontline, with Liam Fox expected to name an unchanged lineup.
As for the visitors, Rocky Bushiri, Maciej Dabrowski, Aiden McGeady and Kevin Nisbet are all set to miss out through injury.
Although there is a short turnaround from Saturday's win over Motherwell, Johnson could opt to use the same starting XI for the fourth consecutive game.
Mykola Kukhareych is still looking for his first Hibernian goal after joining on loan from Troyes in the summer transfer window, and the forward will attempt to open his account when he leads the line on Tuesday.
Dundee United possible starting lineup:
Eriksson; Smith, Edwards, McMann; Freeman, Sibbald, Levitt, Behich; Middleton; McGrath, Watt
Hibernian possible starting lineup:
Marshall; Cadden, Porteous, Hanlon, Cabraja; Boyle, Newell, Kenneh, Campbell, Youan; Kukharevych