But this wasn’t an afternoon without its anxieties for manager Ange Posteocglou and the home fans at Celtic Park before Cameron Carter-Vickers marked his debut with the goal which finally broke County’s resistance midway through the second half.
Until the on-loan Tottenham centre-half’s shot took a wild deflection to loop over visiting goalkeeper Ross Laidlaw, a combination of poor finishing from Celtic and intelligent defending from County had the outcome very much in doubt.
In the end, it was convincing enough from Postecoglou’s perspective as two goals from Albian Ajeti – his first since February – ensured no more ground was lost in these embryonic stages of the title race.
Carter-Vickers could certainly feel satisfied with his afternoon’s work. While he appeared to feel the pace of the contest at times, he contributed robustly to a clean sheet which was threatened more than once by County’s counter-attacking threat.
Portuguese winger Jota had a less notable debut. The Benfica loanee showed some neat touches but was let down too often by the quality of his final shot or cross, including one almost comical attempt at goal which went out for a throw-in.
Laidlaw made one fine save for County in the first half, touching Liel Abada’s shot onto the crossbar, but it was generally Celtic’s wastefulness which was the biggest barrier to them.
Jota blazed over from a good position, while Abada saw another effort deflected onto the bar before being guilty of a horrible miss from inside the six yard box after being set up by Tom Rogic.
Celtic had to replace Greg Taylor with Adam Montgomery early in the second half when the Scotland squad left-back suffered a recurrence of a shoulder injury.
While they continued to dominate possession, it was with an increasing lack of cohesion and amidst growing signs of frustration in the stands.
The mood changed in the 64th minute, however, when Carter-Vickers decided to have a go from distance. Without the diversion it took off a defender, it would have been unlikely to greatly trouble Laidlaw who was helpless to prevent the ball spinning over his head into the net.
County substitute Dominic Samuel should have equalised four minutes later but sent his close range header from Regan Charles-Cook’s cross straight at Joe Hart.
That miss was punished by Celtic who went straight up the pitch to make it 2-0. Ajeti had hardly enjoyed the most impressive of days, his lack of movement underlining just how much Celtic missed the injured Kyogo Furuhashi.
But the Swiss international did what was required of him when he headed home Abada’s perfect cross from the right and then, with five minutes remaining, was on the spot again to nod in from close range after substitute James McCarthy’s effort rebounded off the bar.
Celtic (4-3-3): Hart, Juranovic, Carter-Vickers, Starfelt, Taylor (Montgomery 48); Rogic (McCarthy 78), McGregor (Soro 68), Turnbull; Abada, Ajeti, Jota. Subs not used: Bain, Urhoghide, Shaw, Welsh.
Ross County (4-2-3-1): Laidlaw, Burroughs (Watson 73), Clarke, Baldwin, B.Paton; Spittal, Tillson; A.Samuel (H.Paton 46), Callachan, Charles-Cook; White (D.Samuel 63). Subs not used: Cancola, Robertson, Hungbo, Maynard-Brewer.