Substitute Leigh Griffiths' sizzling second-half free-kick was enough to beat Ross County and extend Celtic's own British unbeaten domestic record to 64 games.
The Ladbrokes Premiership leaders had found the Staggies difficult to break down at the Global Energy stadium in Dingwall.
After the hour mark Hoops boss Brendan Rodgers turned to the bench for help from the Scotland striker, who came on with Jonny Hayes.
And when Griffiths got his opportunity from a free-kick in 77 minutes, he curled it trademark style past Stages keeper Aaron McCarey to give the Hoops a narrow win and set them up for the Champions League game against Paris St Germain in France on Wednesday night.
Left-back Kieran Tierney made his 100th appearance for Celtic in an unchanged side with fit-again Griffiths and defender Jozo Simunovic on the bench.
Owen Coyle's side were also unchanged and enjoyed a rather stress-free first-45 minutes which provided few talking points.
Celtic keeper Craig Gordon had to race out quickly to thwart Staggies midfielder Michael Gardyne in the opening stages where the visitors practised their passing game, in no apparent hurry to get to the County goal.
There were also signs of slackness in the Hoops play and in the 13th minute, after defender Nir Bitton had conceded possession, wide-man Davis Keillor-Dunn curled a shot over the bar from 20 yards.
The league leaders slowly gained control and in the 23rd minute midfielder Stuart Armstrong played in fellow midfielder Callum McGregor but he appeared to have the ball nicked away from his toe by Christopher Routis as he set himself to shoot, although the Parkhead player appealed for a penalty.
Celtic defender Mikael Lustig found the side-netting from a McGregor corner at the start of the second-half and the Hoops first shot on target came in the 55th minute from Moussa Dembele which McCarey gathered with ease.
At the other end, Gordon got down to his right-hand post to save a 25-yard free-kick from Routis before Rodgers brought on Griffiths and Hayes on for McGregor and James Forrest.
The Highlanders began to sense there was more than a draw on offer and broke with increasing purpose and confidence.
Celtic, for their part, could not get out of their slumber.
However, when Jim O'Brien was booked for a foul on Armstrong, it gave Griffiths an opportunity to make his mark that he accepted readily, curling his free-kick high past McCarey.
The goal allowed the treble-winners to relax and midfielder Olivier Ntcham, on for Dembele, cracked the post with a drive from the edge of the box, and Scott Sinclair missed the target with a good chance before the end, with a County claim for handball against Dedryck Boyata in the Celtic box ignored.