The hosts twice came from behind as a ferociously-contested fifth north clash of the season finished 2-2 in normal time.
After a scoreless extra 30 minutes, Caley Thistle rattled in all five of their kicks with Nathan Austin hitting the last to seal it.
But it was Ridgers’ save to his left from unlucky County substitute Declan McManus which made the difference.
John Robertson’s men will now fancy their chances of a Hampden Park semi-final after jubilant celebrations in the pouring rain in Inverness
The form-book pointed to Ross County’s passage, with the team from 14 miles along the road unbeaten in the last eight Highland derbies.
Equally, County’s consistency – top of the league with only three defeats since August – stood in stark contrast with the hosts’ erratic campaign of highs and lows.
Caley Thistle made three changes from the team beaten miserably at Dunfermline at the weekend with influential Liam Polworth shrugging off injury concerns to return.
County made five changes from the side that beat East Fife to reach the Irn-Bru Cup final, the most surprising switch being Jamie Lindsay losing his starting place to January signing Lewis Spence.
Despite a very bright start, the first half represented a microcosm of Caley Thistle’s season – with promising play too easily undone.
Home tails were up at the outset and, after 11 minutes, Jordan White’s dangerous ball across from the left had County keeper Scott Fox scrambling to palm away from Polworth’s reach.
Moments later, the same home midfielder flashed a long-range strike just high and wide of target.
But Caley Thistle suffered an early sickener as ex-Rangers winger Tom Walsh – with nine goals this season – limped off injured. On came 17-year-old Hearts loanee Anthony McDonald.
County’s first attack produced the evening’s first goal. Marcus Fraser slipped a pass down the right for Josh Mullin who hung a wonderful ball across the penalty box.
From eight yards, the imposing figure of Ross Stewart leapt to send a downward header bouncing up into the roof of the net for his third successive derby goal.
A McDonald attempt deflected wide but, towards the break, County established control.
It took a brilliant save from Ridgers to spare the hosts a heavier half-time deficit, with the keeper’s fingertips diverting a Mullin strike from the right just wide of the far post.
Early in the second half, there were howls for a penalty from the home camp as Polworth nodded a Carl Tremarco delivery back across the box. As Doran went to head close in, the hosts felt County captain Fraser had shoved him to the ground. But they were back in business after 56 minutes in the simplest of fashions.
Polworth won a corner on the right off Kenny van der Weg’s challenge and Joe Chalmers’ dipping corner found the unchallenged Jordan White smashing a six-yard header past Fox. A couple of minutes later, Polworth’s strike from the edge of the box was superbly saved down low by Fox at the near post.
It proved an electrifying, frenzied finish to the match.
Fresh home appeals for a penalty when White went down proved prelude to County restoring the lead. County scorer Stewart knocked on a free-kick and Gardyne, pictured, sliced into the penalty area past a couple of challenges and then thrashed a shot between Ridgers and the near post. But there was more to come. Caley Thistle drew level with nine minutes left, Polworth’s defence-splitting pass finding White racing in to hammer his second past Fox from 16 yards.With three minutes left, County were creaking as a White head-flick sent substitute Nathan Austin racing in on Fox only for the keeper to push the ball against his post.
A Tremarco effort was knocked off the line amid the late mayhem, but extra-time beckoned.