The Staggies produced a solid performance on their Scottish Premier League bow, and restricted Motherwell to very few chances at the revamped Global Energy Stadium in Dingwall.
Motherwell had the better of possession but last season's First Division champions looked a threat from set-pieces with some dangerous deliveries by Iain Vigurs and Richard Brittain offering opportunities to tall defenders such as Ross Tokely and Grant Munro.
As they had done during their 2-0 defeat by Panathinaikos in their Champions League qualifier on Tuesday, Motherwell lacked a cutting edge despite confidence on the ball.
Their best chance fell to Michael Higdon just before the interval but the striker headed over from close range.
While it was an unspectacular start to top-flight life for the former Highland League club, who were admitted to the Scottish Football League in 1994, they seemed happy with a point against last season's third-placed side.
County's renamed stadium underwent a £1.7million summer transformation to meet SPL criteria for 6,000 seats, but the former Victoria Park has retained much of its original character and the 4,828 crowd hailed the unfurling of the First Division title flag.
The Motherwell fans were also in party mood after County paid for their official supporters' association coaches.
Although the home side were SPL newcomers, each member of their starting line-up had previous top-flight experience, including former Inverness defender Tokely, who made the short trip north in the summer.
Manager Derek Adams modified his tactics by playing Colin McMenamin up front alone with Martin Scott, back on loan from Hibernian, supporting from a five-man midfield.
McMenamin got a weak header on target early on, but Motherwell quickly settled into a decent passing rhythm with the home side sitting deep.
The visitors were being restricted to long-range efforts although Jamie Murphy, playing up front with Omar Daley wide left almost opened the scoring on the half-hour mark, when his ball into the box curled just wide.
Motherwell soon put themselves under pressure by conceding some cheap free-kicks inside their own half.
One of those led to a chance for Munro, as he headed Brittain's delivery towards the roof of the net, to be denied by Darren Randolph.
Higdon had two chances before the break from Tom Hateley crosses. The full-back chipped a cross over goalkeeper Michael Fraser after some patient build-up play, but Tokely beat Higdon to the ball to head over.
Higdon had a better chance from the resulting corner but headed over from underneath the bar with his back to goal.
Motherwell continued to have the better of possession after half-time but were unable to carve out chances against an organised County side.
County remained a threat at set-pieces and Scott Boyd headed wide from an inswinging corner by Iain Vigurs.
Motherwell brought on Henrik Ojamaa with 20 minutes left and he livened up their strikeforce with some direct running, but there was no end product and they will need to sharpen up their attacking play if they are to pull off a shock in Athens on Wednesday.
The hosts continued to play on the break and they survived some late pressure to claim their first SPL point.