The Lions have won all five of their League Cup matches this season, scoring 19 goals in the process, while the Staggies defeated 19-time champions Celtic in the previous round.
Scott Robinson came off the bench to put the Lions in front midway through the second half and they were able to hold on for the three points, claiming their second away victory of the season.
The appointment of interim boss David Martindale has had an instant impact, with Livingston scoring eight times in three matches, including four goals in their Scottish League Cup victory over Ayr United.
That result has set up Wednesday night's match with Ross County, whom they have beaten in the last two home matches played against them by an aggregate score of 5-0.
Another victory over the Staggies would send them into their first League Cup semi-final since the 2005-06 campaign.
Ross County's miserable league form continued last weekend as they lost 2-0 away at Aberdeen, which was their 10th defeat of the season.
Their Scottish League Cup form however has been much better as the Staggies have won all four of their Group D games as well as taking advantage of Celtic's woes to secure a brilliant 2-0 away victory, sending them into the quarter-finals.
The last time the Staggies faced Livingston was at Victoria Park last month with the two teams seeing out a 1-1 in the league.
Ross County, who are the last team to win the League Cup aside from Celtic, would book their place in the semi-finals for the first time since 2015-16 with victory at the Tony Macaroni Arena.
Livingston Scottish League Cup form: WWWWW
Livingston form (all competitions): WWLWWW
Ross County Scottish League Cup form: WWWWW
Ross County form (all competitions): WWLWLL
Injuries have mounted for Ross County heading into the Christmas period with six players currently ruled out.
Livingston possible starting lineup:
McCrorie; Devlin, Fitzwater, Guthrie, Serrano; Bartley, Sibbald; Mullin, Pittman, Forrest; Poplatnik
Ross County possible starting lineup:
Laidlaw; Randall, Donaldson, Iacovitti, Reid; Kelly, Paton, Vigurs, Tillson, Charless-Cook; Stewart
We say: Livingston 1-0 Ross County
Ross County have never beaten Livingston in a League Cup match and despite securing a surprise victory against Celtic in the last round, they may find things difficult as the home side have turned their form around and seem to have enough quality to edge out their opponents and reach the semi-finals.