Inverness boss Terry Butcher was a relieved man as his side edged past Ross County in their William Hill Scottish Cup fourth-round replay on a sub-zero night at the Caledonian Stadium.
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Billy McKay opened the scoring for Caley Thistle from the penalty spot after nine minutes, but a sublime effort by Iain Vigurs levelled matters four minutes before the interval.
But Inverness booked a fifth-round tie away to Kilmarnock when McKay took his tally for the season to 13 goals by curling home an excellent winner in the 54th minute.
Butcher said: "It was a great game to win. I'm just delighted we're through. Ross County put us under a lot of pressure and we certainly didn't get an easy time of it.
"However, it was a great bit of quality by Billy McKay. It was a goal worthy of winning any game."
County boss Derek Adams claimed his side were hard done by after holding their Highland neighbours to a 3-3 draw in the first game and then giving as good as they got tonight.
And he also felt the decisions went against his team.
He said: "Inverness get a penalty in the first half, but then Grant Munro doesn't get awarded one in the second half. The decisions haven't gone for us.
"We were the better team, We had more possession and opportunities. (Goalkeeper) Mark Brown had one save to make, but has picked the ball out of the back of the net twice.
"We've had a couple cleared off the line and their goalkeeper has made saves.
"It's hard to take because we were camped in their half for the whole second period."