Match ends, Celtic 3, Ross County 0.
Manager Ange Postecoglou said Celtic required "perseverance" to earn a hard-fought Scottish Premiership win against a stubborn Ross County.
County frustrated the hosts until the 64th minute, when debutant centre-back Cameron Carter-Vickers' long-range strike deflected over Ross Laidlaw.
Albian Ajeti headed in six minutes later to kill the game, before nodding in a third to lift Celtic to fifth.
"We needed a goal to open to them up," Postecoglou said.
"When you don't get it, it gives them confidence and they defended well. We've seen in other games if we score early it opens the game up. The info we gave to the whole group at half-time was 'stick to our principles'."
County drop to 11th and are still without a league win this term.
But Malky Mackay will be encouraged by his side's shape and organisation for over an hour of the contest.
As for Celtic, Postecoglou's men put distractions surrounding chief executive Dom McKay's shock departure to one side as they eventually broke down a resolute visiting defence to secure a third straight home league win.
The hosts also had to deal with the absence of Kyogo Furuhashi, who is out for at least a month with a knee injury.
Expectation was placed on the shoulders of debutant winger Jota and he was living up to the hype early on, having a shot from distance saved and a close-range effort sail over either side of Liel Abada having an attempt parried onto the bar.
Celtic continued to probe and a free-flowing breakaway resulted in Ajeti having a tame effort saved, before David Turnbull put a 25-yard effort just wide of the near post.
County put in a power of relentless work to limit Celtic's chances and began to pose a threat of their own when Blair Spittal fired in a dangerous cross to no avail, and Jack Burroughs then lashed wide when a cross was the better option.
Up the other end, Abada struck the woodwork again with a deflected effort before firing a near-post finish into the side net. And there was a sense that a bit of frustration was creeping in, with Abada, Josip Juranovic and Jota firing efforts off target.
It seemed it would take something special or fortuitous to break County down and it was the latter as Cameron-Vickers' deflected effort looped over a helpless Laidlaw.
County did not go down without a fight as Joe Hart had to pull off a smart save to deny substitute Dominic Samuel's header, but the contest was over when Abada's inch-perfect delivery was headed in by Ajeti.
The Swiss striker added his second, and Celtic's third, when he nodded in a close-range rebound.
Man of the match - Jota
What did we learn?
Celtic did not allow the media circus around McKay's departure, Kyogo's absence, and a stubborn County to derail their day.
Their past two home league games have seen Postecoglou's side dismantle Dundee and St Mirren 6-0, but they had to show a patient side of their game on Saturday to gain three valuable points.
County's start to the season has been unforgiving, with their first five league games coming against last season's top five.
It was looking bleak for Mackay, but a valuable point at Aberdeen a fortnight ago and a promising display for large spells at Celtic will give the County boss hope going into a home game against Hearts next Saturday.
What did they say?
Ross County manager Malky Mackay: "I've got a sense of disappointment, but we've got to get over that. The game plan was working.
"In the first half we had a couple of chances across their goal that on another day we might be more clinical with. But I'm seeing a group that are beginning to grow and play the way I want them to."
Celtic go to Seville to face Real Betis on Thursday (17:45 BST) in their opening Europa League game, before a trip to Livingston in the league next Sunday (15:00). County are at home to Hearts next Saturday (15:00).
- 3TaylorSubstituted forMontgomeryat 48'minutes
- 18RogicSubstituted forMcCarthyat 78'minutes
- 42McGregorSubstituted forSoroat 68'minutes
- 17Neves Filipe
- 18BurroughsSubstituted forWatsonat 73'minutes
- 24PatonBooked at 61mins
- 9SamuelSubstituted forPatonat 45'minutes
- 26WhiteSubstituted forSamuelat 63'minutes
- Don Robertson
- Shots on Target
Second Half ends, Celtic 3, Ross County 0.
Offside, Ross County. Keith Watson tries a through ball, but Dominic Samuel is caught offside.
Offside, Ross County. Keith Watson tries a through ball, but Ross Callachan is caught offside.
Foul by Jota (Celtic).
Keith Watson (Ross County) wins a free kick in the defensive half.
Attempt saved. Harrison Paton (Ross County) left footed shot from the left side of the box is saved in the centre of the goal. Assisted by Ross Callachan.
Foul by Ismaila Soro (Celtic).
Dominic Samuel (Ross County) wins a free kick in the defensive half.
Adam Montgomery (Celtic) wins a free kick on the left wing.
Foul by Blair Spittal (Ross County).
Goal! Celtic 3, Ross County 0. Albian Ajeti (Celtic) header from very close range to the centre of the goal.
Attempt saved. James McCarthy (Celtic) header from the centre of the box is saved in the top centre of the goal. Assisted by David Turnbull with a cross.
Attempt blocked. Liel Abada (Celtic) left footed shot from outside the box is blocked.
Ismaila Soro (Celtic) wins a free kick in the defensive half.
Foul by Regan Charles-Cook (Ross County).
Attempt blocked. Blair Spittal (Ross County) right footed shot from outside the box is blocked. Assisted by Ross Callachan.
Substitution, Celtic. James McCarthy replaces Tomas Rogic.
Attempt missed. David Turnbull (Celtic) right footed shot from outside the box is close, but misses to the left. Assisted by Liel Abada.
Foul by Tomas Rogic (Celtic).