Match ends, Celtic 2, Ross County 0.
Leigh Griffiths remains "an asset" for Celtic, says manager Neil Lennon after the striker scored on his first Premiership start of the season.
The Scotland international looped in a well-placed header to add to a first-half strike from David Turnbull as Ross County were swept aside.
Celtic stay 16 points behind Rangers, having played three fewer matches.
"It's a good 80 minutes into his legs and he could have had a hat-trick," Lennon told BBC Scotland.
"Griff is never short of confidence. He needs to get sharper and he'll say 'well, you need to play me'. I think the more he plays and stays fit he'll be an asset for us going forward."
The clamour to remove Lennon reached fever pitch following a League Cup defeat at home against County last month, but the pressure on the Celtic boss has eased in recent weeks.
Sunday's dramatic Scottish Cup success completed a quadruple treble of trophies and the champions are now five games unbeaten in all competitions.
There were further signs of improvement in this one-sided contest, too. Griffiths and Odsonne Edouard were paired together up front, with the Frenchman given a freer role to go looking for the ball.
Both were lively, with Edouard shooting just wide in the first half and Griffiths squandering two good chances shortly before he got his goal.
That arrived on the hour when he was given time to steer home a delivery from the right from Ryan Christie.
Griffiths, who scored as an extra-time substitute and tucked in a shoot-out penalty against Hearts, had earlier delayed a good shooting opportunity, while Ross Laidlaw saved after an appalling back-pass from Iain Vigurs presented Griffiths with a one-on-one.
The breakthrough had come after 24 minutes when Jeremie Frimpong turned Josh Reid inside out before his cut-back from the bye-line was turned in by Turnbull.
Bottom-of-the-table County battled diligently under new manager John Hughes but seldom threatened.
The visitors spent most of the time defending their own penalty area but did have one good sight of goal early on, when Ross Stewart, who went off injured before half-time, glanced a header wide.
Man-of-the-match - David Turnbull
What did we learn?
Griffiths and Edouard have proven their prowess as a partnership before and, while the former was undoubtedly rusty, he got a valuable 80-minutes under his belt and tucked away his fifth goal of the season with a calm assurance.
With County sitting deep, Turnbull and Christie were busy as the champions looked for gaps in a packed defence, although some of the play out from the back remains a bit ponderous.
The home defence were rarely troubled but a clean sheet will be welcome and there were no signs of the panic witnessed at Hampden on Sunday and in several other outings this season.
What did they say?
Celtic manager Neil Lennon: "It's another step in the right direction. I thought we should have won the game by a lot more but I'm very pleased with the freshness the boys who came in today brought to the team. The was a good zest about us."
Ross County manager John Hughes: "Our organisation, the distances between players, our willingness to get stuck in and fight for the cause; I think that was evident. The disappointment is I'd like to have created more chances, laid a glove on them a little bit, and I'd like to have been better on the ball."
Celtic visit Hamilton Academical on Boxing Day (15:00 GMT), while Ross County are at home to St Mirren (15:00) looking to end a run of 11 league games without victory.
- 17ChristieSubstituted forRogicat 72'minutes
- 14TurnbullSubstituted forNtchamat 71'minutes
- 9GriffithsSubstituted forAjetiat 81'minutes
- 22EdouardSubstituted forJohnstonat 72'minutes
- 6DraperSubstituted forTillsonat 76'minutes
- 11VigursSubstituted forMckayat 76'minutes
- 7GardyneSubstituted forHyltonat 45'minutes
- 27StewartSubstituted forShawat 34'minutes
- Euan Anderson
- Shots on Target
Second Half ends, Celtic 2, Ross County 0.
Attempt saved. Jermaine Hylton (Ross County) right footed shot from the centre of the box is saved in the centre of the goal.
Foul by Ismaila Soro (Celtic).
Oli Shaw (Ross County) wins a free kick in the defensive half.
Attempt saved. Oli Shaw (Ross County) right footed shot from outside the box is saved in the bottom left corner. Assisted by Billy Mckay with a headed pass.
Attempt saved. Olivier Ntcham (Celtic) right footed shot from the centre of the box is saved in the bottom right corner. Assisted by Michael Johnston.
Offside, Ross County. Stephen Kelly tries a through ball, but Callum Morris is caught offside.
Foul by Kristoffer Ajer (Celtic).
Oli Shaw (Ross County) wins a free kick on the right wing.
Substitution, Celtic. Albian Ajeti replaces Leigh Griffiths.
Offside, Celtic. Olivier Ntcham tries a through ball, but Leigh Griffiths is caught offside.
Attempt blocked. Michael Johnston (Celtic) left footed shot from the centre of the box is blocked. Assisted by Tomas Rogic.
Foul by Leigh Griffiths (Celtic).
Callum Morris (Ross County) wins a free kick in the defensive half.
Substitution, Ross County. Jordan Tillson replaces Ross Draper.
Substitution, Ross County. Billy Mckay replaces Iain Vigurs.
Foul by Tomas Rogic (Celtic).
Iain Vigurs (Ross County) wins a free kick in the defensive half.
Attempt blocked. Olivier Ntcham (Celtic) right footed shot from the centre of the box is blocked. Assisted by Jeremie Frimpong.