Midfielder Craig Sibbald gave the Lions the perfect start after four minutes with a goal that had a question of offside in the build-up before attacker Alan Forrest took advantage of a fluke chance after 23 minutes to head in a second, which proved enough for a last-four berth.
It was a cold and wet night when little went right for the Premiership's bottom side who had sensationally knocked out holders Celtic in the previous round, but in the end it was a deserved win for the Lions who go from strength to strength.
David Martindale, the club's head of football operations, has now won four out of four matches since taking over as interim head coach following Gary Holt's departure and must have a great chance of becoming permanent boss.
The home side started ominously with Josh Mullin firing a free-kick from 25 yards straight into the arms of Staggies goalkeeper Ross Laidlaw.
Minutes later, Livi went ahead when Sibbald ran on to Scott Robinson's pass and slipped the ball past Laidlaw.
Robinson, back in the side for Matej Poplatnik, had looked offside but got involved after County right-back Regan Charles-Cook took a touch.
After checking with his linesman, who had flagged offside and taken his flag down again, referee Steven McLean confirmed the goal.
The Staggies hit back almost right away with striker Ross Stewart's flick from a corner hitting the side netting.
The Highlanders were forced in to a substitution after 20 minutes when Charles-Cook limped off to be replaced by Coll Donaldson, just before the Lions added a second.
County defender Callum Morris' attempted clearance close to the by-line came off Robinson and looped over Laidlaw allowing Forrest to head in from a couple of yards for his 10th goal of the season, the seventh in the competition.
Stuart Kettlewell's side kept going and in the 35th minute home goalkeeper Max Stryjek blocked a drive from Stewart before captain Iain Vigurs curled a free-kick just off target, after Livi's Jon Guthrie was shown a yellow for a foul on Billy Mckay, 20 yards from goal.
Then a County penalty appeal for a foul by Scott Pittman on Harry Paton was ignored before Mckay's weak shot with only Stryjek to beat was comfortably saved.
The West Lothian side had the best chances in the second half.
Defender Jack Fitzwater headed a Mullen corner just past the post, Robinson rattled the crossbar with a terrific volley and Julien Serrano struck the near post with a low drive after a swift break.
And in the end, County – for all their effort – were left frustrated.