Ross County 0 - 2 Celtic
Celtic booked their place in the quarter-finals of the Scottish Communities League Cup after seeing off the challenge of Ross County.
County, looking to repeat their 2010 Scottish Cup win over Celtic, fell behind when Gary Hooper tapped home on the line after 13 minutes.
The hosts almost levelled when Michael Gardyne's piledriver rattled the post.
Scott Boyd's own goal gave Celtic a healthier lead and Neil Lennon's side were comfortable thereafter.
Celtic join Scottish Premier League contemporaries Dundee United, Hibernian, Kilmarnock, St Mirren, Division One Falkirk and Second Division East Fife in the last eight.
The visitors moved into the lead after Charlie Mulgrew's corner had been cleared and then retrieved by Anthony Stokes.
The striker's cross back into the danger area was headed down by Joe Ledley to the predatory Hooper, who added the final touch.
Celtic were having some success from Mulgrew's deliveries, County taking several attempts to clear after another inswinging corner from the left-sided player.
County's fans were on their feet moments later, only to have their celebrations cut short.
Michael Gardyne hovered on the D of the penalty area as the Celtic defence cleared and smacked a volley against the base of Fraser Forster's left-hand post.
Goalkeeper Michael Fraser was quick off his line to block an effort by Ledley after the Welshman had been put through by Hooper.
Colin McMenamin was unable to get enough purchase on a shot that Forster claimed but the Highlanders' ability to get the ball forward quickly was causing Celtic problems.
However, Celtic doubled their lead seven minutes after the break.
Hooper forced a save from Fraser but County failed to clear their lines and Stokes's low cross was turned into the net by Boyd.
Pressure continued to be exerted on the Ross County backline and a late intervention by the experienced Grant Munro averted the danger posed by Forrest.
Celtic retained possession well in the closing stages and Fraser made an excellent save late on to deny substitute Paul George from close range.
Celtic manager Neil Lennon:
"I'm delighted, it wasn't easy. It never is coming to a First Division ground, the conditions were difficult to play in.
"We were very professional and it was exactly the reaction I was looking for from the players.
"The attitude and the manner we approached the game in was what I wanted.
"The football we played at times in the final third was very good. I'm also very pleased with the clean sheet.
"There were some very good individual performances."
Ross County manager Derek Adams:
"We started the game very well. We lost a bad goal but after that Michael Gardyne hit the post.
"In the second half, no complaints. I thought that Celtic thoroughly deserved to win the match.
"We went 2-0 down and there was only one winner after that.
"Celtic were far too strong for us. They're at a different level from us.
"I'm proud of the players and the way they stuck to their task. We caused them problems at times."
Live Text Commentary
Full Time The match has reached full-time.90:00 +1:54
Mark Corcoran takes a outswinging corner to the near post, Joe Ledley manages to make a clearance.90:00 +0:31
Gary Miller takes a shot. Fraser Forster makes a save.88:29
James Forrest takes a outswinging corner to the near post, Michael Gardyne makes a clearance.88:29 Substitution
Substitution Paul George on for Gary Hooper.83:30 Substitution
Substitution Stuart Kettlewell is brought on as a substitute for Colin McMenamin.83:30 Substitution
Substitution (Ross County) makes a substitution, with Mark Corcoran coming on for Paul Lawson.81:37
The official flags Kurtis Byrne offside. Fraser Forster takes the indirect free kick.80:27
Corner taken right-footed by Richard Brittain from the right by-line, clearance made by Victor Wanyama.79:02
Inswinging corner taken right-footed by Richard Brittain from the left by-line, clearance by Daniel Majstorovic.78:21
Unfair challenge on Scott Boyd by Mohamed Bangura results in a free kick. Indirect free kick taken by Michael Fraser.77:41
Free kick awarded for an unfair challenge on James Forrest by Paul Lawson. Indirect free kick taken by Fraser Forster.77:41 Substitution
Substitution (Celtic) makes a substitution, with Mohamed Bangura coming on for Anthony Stokes.75:40
Colin McMenamin is flagged offside by the assistant referee. Charlie Mulgrew takes the free kick.74:36
Inswinging corner taken by Richard Brittain from the left by-line, Victor Wanyama makes a clearance.74:36 Substitution
Substitution Iain Vigurs leaves the field to be replaced by Kurtis Byrne.73:40
Charlie Mulgrew is adjudged to have handled the ball. The free kick is delivered left-footed by Iain Vigurs from right channel, Charlie Mulgrew makes a clearance.72:19
The referee blows for offside against Anthony Stokes. Michael Fraser takes the indirect free kick.66:09
Daniel Majstorovic challenges Colin McMenamin unfairly and gives away a free kick. Rocco Quinn takes the free kick.60:12
Gary Hooper takes a shot. Save by Michael Fraser.
Joe Ledley decides to take the corner short, Colin McMenamin manages to make a clearance.58:31
Unfair challenge on Marc Fitzpatrick by James Forrest results in a free kick. Marc Fitzpatrick restarts play with the free kick.55:19
Iain Vigurs concedes a free kick for a foul on James Forrest. Free kick taken by Daniel Majstorovic.51:53
Free kick awarded for a foul by James Forrest on Marc Fitzpatrick. Richard Brittain restarts play with the free kick.50:58 Goal scored
Goal! - Scott Boyd - Ross Co 0 - 2 Celtic Scott Boyd concedes an unfortunate own goal. Ross County 0-2 Celtic.50:15
Gary Hooper takes a shot. Michael Fraser makes a save.46:37
Foul by Gary Hooper on Scott Boyd, free kick awarded. Gary Miller takes the direct free kick.45:01
The second half has started.45:01 Substitution
Substitution Victor Wanyama joins the action as a substitute, replacing Kelvin Wilson.45:00 +0:56 Half time
Half Time The ref blows to signal half-time.44:19
Colin McMenamin takes a shot. Fraser Forster makes a save.41:28
Anthony Stokes takes a shot. Save made by Michael Fraser.39:09
Rocco Quinn gives away a free kick for an unfair challenge on Beram Kayal. Direct free kick taken by Beram Kayal.37:15
The assistant referee flags for offside against Colin McMenamin. Fraser Forster restarts play with the free kick.36:04
Anthony Stokes fouled by Scott Boyd, the ref awards a free kick. Adam Matthews crosses the ball from the free kick right-footed from left wing, Scott Boyd makes a clearance.32:56
Colin McMenamin concedes a free kick for a foul on Kelvin Wilson. Fraser Forster takes the direct free kick.32:20 Booking
Booking Colin McMenamin goes into the book for unsporting behaviour.31:47
Free kick awarded for a foul by Richard Brittain on Adam Matthews. Beram Kayal takes the free kick.31:20
Inswinging corner taken right-footed by Richard Brittain, Kelvin Wilson makes a clearance.30:31
Colin McMenamin fouled by Kelvin Wilson, the ref awards a free kick. Free kick crossed by Iain Vigurs, Daniel Majstorovic manages to make a clearance.24:39
Free kick awarded for a foul by Daniel Majstorovic on Colin McMenamin. Michael Fraser takes the free kick.22:15
Michael Fraser takes the direct free kick.22:15 Booking
Booking Adam Matthews goes into the book.22:12
Foul by Adam Matthews on Michael Gardyne, free kick awarded.20:38
Free kick awarded for a foul by Joe Ledley on Richard Brittain. The free kick is swung in left-footed by Iain Vigurs, clearance made by Daniel Majstorovic.19:35
Michael Gardyne takes a shot from a just insdie the box and hits the post.19:00
James Forrest concedes a free kick for a foul on Marc Fitzpatrick. Michael Fraser takes the direct free kick.17:47
Badr El Kaddouri is ruled offside. Michael Fraser takes the free kick.17:07
Corner taken left-footed by Charlie Mulgrew, clearance made by Scott Boyd.16:36
Anthony Stokes takes a shot. Blocked by Gary Miller.14:09
Richard Brittain gives away a free kick for an unfair challenge on Badr El Kaddouri. Direct free kick taken by Fraser Forster.12:55
The assist for the goal came from Joe Ledley.12:55 Goal scored
Goal! - Gary Hooper - Ross Co 0 - 1 Celtic Gary Hooper finds the net with a goal from close in to the bottom left corner of the goal. Ross County 0-1 Celtic.11:54
Inswinging corner taken from the right by-line by Charlie Mulgrew.10:04
Badr El Kaddouri challenges Rocco Quinn unfairly and gives away a free kick. Iain Vigurs takes the direct free kick.4:56
Free kick awarded for an unfair challenge on Joe Ledley by Colin McMenamin. Direct free kick taken by Fraser Forster.3:42
Badr El Kaddouri challenges Richard Brittain unfairly and gives away a free kick. Gary Miller takes the free kick.1:14
Rocco Quinn fouled by Kelvin Wilson, the ref awards a free kick. Free kick crossed right-footed by Richard Brittain, clearance by Gary Hooper.0:00
The game gets underway.
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