Celtic extended their record unbeaten domestic run to 64 games after an outstanding Leigh Griffiths free-kick broke Ross County’s resolve.
The substitute struck with 12 minutes remaining, sweeping the ball into the top corner from 25 yards out.
Celtic needed a moment of individual poise to secure the victory, since County were dogged and well-organised throughout.
Another substitute, Olivier Ntcham, hit the post as County’s intensity flagged.
The Premiership leaders dominated possession, only to see their attacks break down in the final third, in part through County’s pressing and sound defending, but also through poor decision making and a lacklustre display by Moussa Dembele.
The visitors ought, though, to have been awarded a penalty in the first half, when Christopher Routis kicked Callum McGregor’s foot onto the ball inside the area, but referee Nick Walsh thought the defender had cleared with a clean tackle.
Ross County also claimed for a spot-kick in injury time as the ball brushed Dedryck Boyata’s arm from a long throw.
Individual moments stood out, since the majority of the game was a grind of relentless effort with little sophistication.
Celtic manager Brendan Rodgers selected his strongest starting line-up, even though there is a Champions League assignment in Paris on Wednesday, but his leading players tended to run aground against County’s impressive work-rate.
Dembele, Scott Sinclair and James Forrest were subdued, but it is a measure of the defending champions’ strength that the two substitutes made such an impressive impact.
There was slackness in some of Celtic’s lengthy spells of possession, and the first opportunity of the game came when Michael Gardyne intercepted a pass in midfield and played in Davis Keillor-Dunne, who swept a shot over the bar.
County were the last side to stop Celtic winning an away fixture in the league – holding Rodgers’ side to a 2-2 draw last season – and goalkeeper Aaron McCarey showed confident handling to gather high balls under pressure.
Even so, Celtic were aggrieved not to be awarded a penalty when McGregor burrowed his way through a crowd inside the area only to have his foot clipped by Routis.
The first shot on target did not come until the 55th minute, when McCarey comfortably saved Dembele’s tame effort. Routis then saw a free-kick from distance saved by Celtic goalkeeper Craig Gordon.
As Rodgers pursued the victory, he withdrew the midfielder McGregor for Griffiths, who joined Dembele up front. Celtic were eventually rewarded for their patience and for commitment to a structured game plan.
Sinclair volleyed high and wide from inside the area, while County’s best hope came when Ryan Dow missed his header from a long throw and the ball brushed against Boyata’s arm, but there was to be no reward for their endeavour.