Billy McKay's double secured a win for Inverness in the Highland derby and a place in the Scottish Cup fifth round.
Caley Thistle were ahead after nine minutes, when former Inverness defender Ross Tokely fouled Josh Meekings and McKay slotted in the resulting penalty.
Ross County were back on level terms four minutes from the break with a sublime 22-yard half-volley from former Caley Thistle midfielder Iain Vigurs.
But McKay struck again with a curling drive nine minutes after the break.
County were at least the equal of the side sitting second in the Scottish Premier League for much of the replay at Caledonian Stadium.
However, it was Caley Thistle who secured a fifth-round trip to face SPL rivals Kilmarnock at Rugby Park.
And it was great reward for that stoppage time equaliser in the 3-3 draw at Victoria Park.
Unchanged Inverness started where they left off in the weekend win over Hibs and took the lead when former Inverness stalwart Tokely was adjudged by referee Craig Thomson to have taken down Meekings in the area.
The 24-year-old McKay fired in the opener from the penalty spot.
Influential midfielder Stuart Kettlewell had replaced forward Gary Glen as County manager Derek Adams went for a less adventurous line-up to the one that lost to Motherwell.
That and the freezing conditions in the appropriately dubbed Cold Firm derby probably contributed to the game deteriorating into a battle of attrition as both teams had spells on top but failed to carve out anything to threaten either goal.
It took until the 35th minute for either side to threaten again and Aaron Doran just failed to mark his 50th appearance for Inverness with a goal as he shot narrowly wide.
However, it was County who struck next, Vigurs netting a beautiful equaliser, dinking the ball over charging goalkeeper Antonio Reguero from 25-yards and in off the underside of the crossbar.
Ross Draper might have put the home side back in front on the stroke of half-time, but he screwed his low piledriver just wide from Richie Foran's lay off.
County started brightly after the interval, with Rocco Quinn forcing Reguero into a save.
However, moments later, McKay netted his second of the game with a superb curling strike from just outside the box for his 13th goal of the season and seventh in the last five games.
Vigurs had the opportunity to level the scores after 68 minutes when he connected with a Quinn cross, but the close-range header was straight at Reguero.
Seconds later, County substitute Grant Munro watched as his header was cleared off the line by David Raven.
Colin McMenamin was next to try his luck after being played through by Scott Boyd, but his low effort rippled the side netting.
County substitute Steven Ross headed a Mark Fitzpatrick cross just wide with seven minutes remaining and visiting captain Richie Brittain had the chance to grasp a last-minute equaliser, but it was cleared by Meekings.
Inverness Caledonian Thistle
- 12 Reguero
- 02 Raven
- 03 Shinnie
- 05 Warren
- 14 Meekings
- 04 Tudur-Jones
- 08 Draper Booked
- 09 Foran Booked
- 17 Doran
- 07 McKay (Roberts - 88' )
- 10 Shinnie (Sutherland - 75' )
- 01 Esson
- 32 Cooper
- 21 Polworth
- 18 Sutherland
- 23 Roberts
- 25 Brown
- 03 Fitzpatrick
- 05 Boyd
- 06 Tokely (Munro - 46' )
- 22 Kovacevic
- 07 Kettlewell Booked
- 10 Brittain
- 12 Quinn (Ross - 78' )
- 29 Fotheringham Booked (Cooper - 65' )
- 09 McMenamin
- 11 Vigurs Booked
- 01 Fraser
- 04 Munro
- 21 Cooper
- 24 Ross
- 20 Glen
Live Text Commentary
Full Time The referee signals the end of the game.90:00 +2:00
Free kick taken by Graeme Shinnie.90:00 +2:00 Booking
Booking Stuart Kettlewell receives a caution.90:00 +1:51
Ross Draper fouled by Stuart Kettlewell, the ref awards a free kick.90:00 +0:52
Richard Brittain produces a right-footed shot from just outside the box that goes wide right of the target.89:47
Iain Vigurs delivers the ball from the free kick left-footed from right channel, clearance made by David Raven.89:47 Booking
Booking Richie Foran goes into the book for dissent.89:37
Free kick awarded for an unfair challenge on Richard Brittain by Richie Foran.88:42
Free kick awarded for a foul by Colin McMenamin on Gary Warren. Antonio Reguero restarts play with the free kick.87:47 Substitution
Substitution Billy McKay goes off and Philip Roberts comes on.86:42
Richie Foran concedes a free kick for a foul on Stuart Kettlewell. Free kick crossed by Richard Brittain, Owain Tudur Jones makes a clearance.85:35
Free kick awarded for an unfair challenge on Alex Cooper by David Raven. The free kick is swung in right-footed by Richard Brittain.84:34
Grant Munro takes a shot and cleared the bar.81:19
Richard Brittain takes the inswinging corner, save by Antonio Reguero.80:50
Free kick awarded for a foul by Ross Draper on Richard Brittain. Free kick crossed left-footed by Iain Vigurs from right by-line, clearance by Ross Draper.79:50
Short corner taken by Aaron Doran.79:15
Colin McMenamin is flagged offside by the assistant referee. Free kick taken by Josh Meekings.76:52
The free kick is delivered left-footed by Iain Vigurs from right wing, Foul by Grant Munro on Ross Draper, free kick awarded. Antonio Reguero takes the free kick.76:52 Substitution
Substitution Rocco Quinn goes off and Steven Ross comes on.76:52
Ross Draper gives away a free kick for an unfair challenge on Iain Vigurs.
Gary Warren concedes a free kick for a foul on Iain Vigurs. Richard Brittain takes the free kick.74:26 Substitution
Substitution Shane Sutherland comes on in place of Andrew Shinnie.74:26
Colin McMenamin has an effort at goal from just inside the box that misses to the right of the target.73:08
Inswinging corner taken by Iain Vigurs, save by Antonio Reguero.72:15
Iain Vigurs crosses the ball in from the free kick, comfortable save by Antonio Reguero.72:15 Booking
Booking Ross Draper is cautioned by the ref for unsporting behaviour.72:00
Foul by Ross Draper on Richard Brittain, free kick awarded.69:21
Billy McKay fouled by Mihael Kovacevic, the ref awards a free kick. Antonio Reguero takes the free kick.69:09
Inswinging corner taken left-footed by Iain Vigurs, Richie Foran manages to make a clearance.68:55
Stuart Kettlewell takes a shot. Blocked by David Raven.68:33
Inswinging corner taken from the right by-line by Iain Vigurs, clearance by Ross Draper.67:49
Billy McKay is flagged offside by the assistant referee. Free kick taken by Grant Munro.66:47
Iain Vigurs takes a shot. Save made by Antonio Reguero.64:46
Foul by David Raven on Colin McMenamin, free kick awarded. Richard Brittain takes the free kick.63:54 Substitution
Substitution Mark Fotheringham goes off and Alex Cooper comes on.63:54
Stuart Kettlewell challenges Graeme Shinnie unfairly and gives away a free kick. Centre by Graeme Shinnie, Headed effort from deep inside the penalty area by Ross Draper goes harmlessly over the crossbar.61:41
Effort from 35 yards by Owain Tudur Jones. Save by Mark Brown.57:56
Iain Vigurs concedes a free kick for a foul on Andrew Shinnie. Free kick taken by Josh Meekings.56:05
Free kick awarded for a foul by Richie Foran on Mihael Kovacevic. Free kick taken by Mark Brown.55:32
Foul by Colin McMenamin on Gary Warren, free kick awarded. Direct free kick taken by Josh Meekings.53:51
Assist by Graeme Shinnie.53:51 Goal scored
Goal! - Billy McKay - Inverness 2 - 1 Ross Co Billy McKay grabs a goal from the edge of the area to the top right corner of the goal. Inverness CT 2-1 Ross County.52:38
Shot by Rocco Quinn from 18 yards. Comfortable save by Antonio Reguero.48:38
Josh Meekings takes the direct free kick.48:38 Booking
Booking The referee cautions Mark Fotheringham for unsporting behaviour.48:22
Free kick awarded for a foul by Mark Fotheringham on Aaron Doran.46:27
Andrew Shinnie challenges Stuart Kettlewell unfairly and gives away a free kick. The free kick is swung in right-footed by Richard Brittain.45:01
The referee gets the second half started.45:01 Substitution
Substitution Ross Tokely goes off and Grant Munro comes on.45:00 +0:13 Half time
Half Time The players leave the pitch at half time.44:57
Inswinging corner taken from the left by-line by Aaron Doran.44:38
Shot by Ross Draper. Blocked by Stuart Kettlewell.44:14
The referee blows for offside. Antonio Reguero restarts play with the free kick.42:42
Free kick awarded for a foul by Owain Tudur Jones on Marc Fitzpatrick. Mark Brown takes the direct free kick.40:31
Assist by Mihael Kovacevic.40:31 Goal scored
Goal! - Iain Vigurs - Inverness 1 - 1 Ross Co A goal is scored by Iain Vigurs from outside the area to the top left corner of the goal. Inverness CT 1-1 Ross County.39:19
Marc Fitzpatrick concedes a free kick for a foul on Aaron Doran. Josh Meekings restarts play with the free kick.36:02
Free kick awarded for an unfair challenge on Mark Brown by Aaron Doran. Direct free kick taken by Mark Brown.35:17
Foul by Richie Foran on Richard Brittain, free kick awarded. Direct free kick taken by Richard Brittain.34:48
Aaron Doran has an effort at goal from outside the box which misses left.31:41
Colin McMenamin fouled by Graeme Shinnie, the ref awards a free kick. Direct free kick taken by Scott Boyd.30:33
Free kick awarded for a foul by Richie Foran on Mark Fotheringham. Mark Brown restarts play with the free kick.29:37
The assistant referee flags for offside against Richie Foran. Mark Brown takes the indirect free kick.29:07
Josh Meekings takes the direct free kick.29:07 Booking
Booking Iain Vigurs is cautioned by the ref for dissent.29:03
Free kick awarded for an unfair challenge on Owain Tudur Jones by Iain Vigurs.26:48
Colin McMenamin fouled by Gary Warren, the ref awards a free kick. Ross Tokely takes the free kick.24:08
Stuart Kettlewell is ruled offside. Josh Meekings restarts play with the free kick.22:42
Iain Vigurs concedes a free kick for a foul on Ross Draper. Josh Meekings takes the direct free kick.15:23
Foul by Mihael Kovacevic on Ross Draper, free kick awarded. Direct free kick taken by Antonio Reguero.11:39
Free kick awarded for an unfair challenge on Mihael Kovacevic by Richie Foran. Mark Brown restarts play with the free kick.11:03
Free kick awarded for a foul by Stuart Kettlewell on Owain Tudur Jones. Free kick taken by Josh Meekings.10:00
The referee blows for offside. Free kick taken by Scott Boyd.9:23
Colin McMenamin is penalised for a handball. Antonio Reguero takes the direct free kick.8:47
Andrew Shinnie takes a shot and went wide right of the net.8:08
Assist by Josh Meekings.8:08 Goal scored
Goal! - Billy McKay - Inverness 1 - 0 Ross Co Billy McKay scores a placed penalty. Inverness CT 1-0 Ross County.6:55
Free kick awarded for an unfair challenge on Andrew Shinnie by Marc Fitzpatrick. Aaron Doran crosses the ball in from the free kick, Ross Tokely gives away a Penalty for an unfair challenge on Josh Meekings.6:14
Free kick awarded for an unfair challenge on Richie Foran by Mihael Kovacevic. Graeme Shinnie takes the direct free kick.3:16
The referee blows for offside against Billy McKay. Mark Brown restarts play with the free kick.2:34
Marc Fitzpatrick concedes a free kick for a foul on Andrew Shinnie. Aaron Doran takes the free kick.0:00
The game begins.
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