The Hoops made eight changes from the starting 11 who defeated rivals Rangers in their League Cup clash on Sunday.
The Hoops made eight changes from the starting 11 who defeated rivals Rangers in their League Cup semi-final clash on Sunday.
However, the new-look Hoops had the perfect start at Victoria Park as Patrick Roberts gave them a third-minute lead.
Both sides had chances to add to the scoring before Stuart Armstrong got Celtic's second in the 83rd minute. Substitutes Scott Sinclair and Moussa Dembele added stoppage-time strikes to seal Celtic's eighth win in nine league matches.
"It was a very tough game for us. Ross County are one of the best teams we have played," Celtic boss Brendan Rodgers said. "But I thought our attacking play was very strong and defensively I thought we were excellent as well."
Ross County manager Jim McIntyre felt the scoreline was harsh on his side.
"I think we were in the game and made good opportunities to score," he said.
"We certainly did a lot of things right on the night but Celtic have shown how clinical they can be with their chances."
Only Craig Gordon, Mikel Lustig and Erik Sviatchenko survived from the win over Rangers as Rodgers looked to utilise his squad ahead of crunch clashes with Aberdeen and Borussia Monchengladbach within the next seven days.
The changes didn't seem to disrupt the Hoops as they grabbed an early lead. Armstrong picked Roberts out with a pass and the on-loan Manchester City winger skipped past some challenges as he glided in from the right before sending a low left-foot effort into the bottom corner.
County had a big chance to equalise minutes later when Liam Boyce went clean through after a mistake from Lustig but Gordon was out quickly to block his shot.
Scott Fox then came to the rescue for County at the other end as he got down smartly to save a Ryan Christie strike.
Michael Gardyne fired a shot just wide for the hosts before Fox made a superb diving save to turn Leigh Griffiths' fiercely struck half-volley round the post as play raged from end to end.
County started the second half strongly and came close to a leveller when Chris Burke's blocked shot looped in the air and looked set to trickle over the line, but Gordon recovered to gather the loose ball.
Sviatchenko then missed a big chance to give Celtic some breathing room when he sent a free header wide from close range.
The Hoops had a massive let-off moments later when a Ross County header from a corner crashed off the inside of the post before it was scrambled clear.
Armstrong started a late goal-rush for Celtic as he sent a composed finish past Fox before Sinclair hit a volley past the keeper two minutes into stoppage time.
French striker Dembele continued his fine start to the season as he tapped home the fourth a minute later to follow up his winner in Sunday's Old Firm derby.
Rivals Rangers remain in fifth after a 1-1 draw with St Johnstone at Ibrox. Blair Alston curled a wonderful strike past Wes Foderingham to give Saints a fifth-minute lead but Joe Garner headed the equaliser past Zander Clark in the 37th minute for only his second goal since joining the Gers from Preston.
Dundee remain firmly rooted to the bottom of the table following a 2-0 defeat by Partick Thistle, Kilmarnock moved up to sixth with a 2-0 win over Hearts while Inverness Caledonian Thistle defeated Motherwell 3-0 at Fir Park.