Lisbon Lion John Clark unfurled the 2014/15 championship flag before kick-off - signifying the club's fourth title victory in succession - and Leigh Griffiths started the journey to number five when he opened the scoring from the spot after only four minutes.
However, the striker hobbled off after 19 minutes with an injury which could leave him struggling for the second-leg of the Hoops' Champions League third qualifier against Qarabag in Azerbaijan on Wednesday night.
Midfielder Stefan Johansen doubled Celtic's lead in the 35th minute with a drive after referee Willie Collum had angered the visitors by only showing Parkhead keeper Craig Gordon a yellow card for a 'last man' challenge outside the box on former Celt, Jackson Irvine.
Gordon went on to have a couple of good saves as the Dingwall men tried to battle back, but Celtic were worth for their 2-0 win, although they might have to defend their 1-0 first-leg victory over Qarabag without Griffiths, last season's top scorer.
With Nadir Ciftci and Emilio Izaguirre suspended, Griffiths started in the main striker's role while 18-year-old Kieran Tierney came in at left-back.
County boss Jim McIntyre fielded seven of his summer signings including skipper Andrew Davies who clumsily conceded a penalty with a challenge on Griffiths as the former Hibernian forward tried to reach a Stuart Armstrong pass.
Griffiths slammed the spot-kick under Scott Fox, another Staggies new boy, but he could not shake off the knock apparently picked up winning the penalty and was replaced by Stefan Scepovic.
Another talking point came in the 22nd minute when County playmaker Ian McShane sent Irvine clean through on goal, to the left of the penalty area.
The midfielder, signed permanently in the summer after a loan period at the Dingwall club, was tripped by Gordon just outside the box.
The Celtic fans breathed a sigh of relief when referee Collum only produced a yellow card with County players claiming it had been an obvious goalscoring opportunity.
Gordon saved the resultant free-kick from McShane down at his right-hand post and the visitors came close again on the half-hour mark when Craig Curran drove just wide from the edge of the box.
However, when Johansen took a pass from Gary Mackay-Steven 12 yards before rifling past Fox, the points looked safe.
County came out after the interval, though, showing some enterprise and Gordon made good blocks from Curran and substitute Raffaele De Vita, who had replaced Stewart Murdoch.
But Celtic threatened too.
In the 69th minute Fox had to concede a corner with a tremendous finger-tip save from a long-range thunderbolt from Kris Commons, on for Johansen.
As the home side stepped up the pressure again, the former Derby midfielder drove past the far post and was then denied again by Fox before the game petered out to what was perhaps an inevitable conclusion.
Source : PA
Source: PA