Match ends, Ross County 0, Hibernian 1.
Hibernian celebrated a first-ever win over Ross County to book their place in the last 16 of the Scottish Cup.
Danny Handling's low first-half drive was enough for the visitors after good footwork from Liam Craig set him free in the box.
Hibs had to play the last 20 minutes a man down after Paul Cairney picked up a second yellow card for simulation.
However, the home side could not make any inroads and the Leith men comfortably held on.
The result was Butcher's first win since taking over the Easter Road club. It will be even more satisfying for the Englishman after failing to pick up a win at Victoria Park during his time as Inverness Caledonian Thistle manager.
County manager Derek Adams will be desperately disappointed his side rarely looked like scoring, even with an extra man.
Defender Steven Saunders was available following suspension, but Adams kept faith with the same side that drew 2-2 with Hearts, with Richard Brittain still available with his ban yet to begin.
Summer signing James Collins replaced Paul Heffernan in the Hibs starting line-up after the latter failed to recover from the thigh injury suffered last week, while Michael Nelson was on the bench after his recovery from a broken cheekbone.
Despite the fast pace of the opening exchanges, neither side was able to take control of the game and it took until 23 minutes for the first real test for either goalkeeper; Cairney firing a vicious shot into the hands of former Hibee Mark Brown.
Hibs opener was almost rugby-esque, with the home side thundering into challenges to keep pushing play further back.
However, Craig eventually battled his way through, finding Handling free on the right and he fired low past Brown.
County suffered a further blow before half-time when Swiss defender Branislav Micic was carried off after going over on his ankle.
Hibs remained the more likely side in the second period, with a solid defence rarely being tested by their hosts.
They could have been 2-0 ahead when a mistake by Brittain gifted Scott Robertson the opportunity to have a free strike at goal, but his shot lacked any real power.
That sparked life into Adams' men. Rocco Quinn almost squeezed the ball into the net as County raced forward on the counter attack before Kevin Luckassen rattled the post with a header from Graham Carey's cross.
The game was turned in its head when Cairney was given a second yellow card.
After drifting by two blue shirts, he only had the goalkeeper to beat but hit the deck with the referee deeming it was a dive without contact.
Despite the one-man deficit, Hibs continued to look for a second and, when substitute Steven Saunders pulled up with an injury, that allowed Butcher's men to storm forward, but Lewis Stevenson's shot was deflected just over.
County had the ball in Hibs box plenty of times but rarely looked like finding the net and their winless run now stretches to five games.
Hibs manager Terry Butcher: "It wasn't the best of football matches - it was a gritty cup tie, but I'm delighted with the win.
"The players showed a level of fitness today and they showed some skill as well, when they get the ball down and pass it.
"We've seen different qualities in the side today we didn't know were there. They keep on surprising us.
"Ross County had one chance when Luckassen hit the post, while Ben Williams hasn't got a save to make.
"For the second week running he's been kept inactive, and we've kept a clean sheet.
"I thought Paul Cairney's second yellow was extremely harsh. It was a goal kick or a penalty, and that's it. There was contact, he's got a big mark on his shin where contact was made."
Ross County boss Derek Adams: "I thought we were very poor today - over the 90 minutes we didn't deserve to go through in the cup.
"We've had a few injury problems but there was no cohesion in the team - it was a lacklustre performance.
"There wasn't much chances in the game, Hibs didn't create many chances either.
"From our from our point of view the choice of passes and the way we played wasn't good enough."
- 4KettlewellBooked at 90mins
- 15GlenSubstituted forMaatsenat 64'minutes
- 6MicicSubstituted forSaundersat 43'minutes
- 11De Leeuw
- 10QuinnSubstituted forKovacevicat 67'minutes
- 8RobertsonSubstituted forTudur-Jonesat 67'minutesBooked at 85mins
- 11CairneyBooked at 71mins
- 19HandlingSubstituted forCaldwellat 80'minutesSubstituted forTaiwoat 90+3'minutes
- 16StevensonBooked at 33mins
- Craig Thomson
- Shots on Target
Second Half ends, Ross County 0, Hibernian 1.
Stuart Kettlewell (Ross County) is shown the yellow card.
Substitution, Hibernian. Tom Taiwo replaces Ross Caldwell.
Corner, Ross County. Conceded by Jordan Forster.
Owain Tudur-Jones (Hibernian) is shown the yellow card.
Richard Brittain (Ross County) wins a free kick in the attacking half.
Foul by Owain Tudur-Jones (Hibernian).
Foul by Graham Carey (Ross County).
James Collins (Hibernian) wins a free kick on the right wing.
Corner, Hibernian. Conceded by Steve Saunders.
Substitution, Hibernian. Ross Caldwell replaces Daniel Handling.
Corner, Hibernian. Conceded by Scott Boyd.
Attempt blocked. Lewis Stevenson (Hibernian) left footed shot from the left side of the box is blocked.
Corner, Ross County. Conceded by Lewis Stevenson.
Second yellow card to Paul Cairney (Hibernian).
Substitution, Ross County. Mihael Kovacevic replaces Rocco Quinn because of an injury.
Substitution, Hibernian. Owain Tudur-Jones replaces Scott Robertson.
Scott Boyd (Ross County) wins a free kick on the left wing.
Foul by James Collins (Hibernian).