The Highland outfit grabbed a draw against the SPL champions as they chase neighbours Inverness CT in the race for European football in their debut season in the top flight
Anthony Stokes put the Parkhead side into an early lead but the much-changed SPL champions couldn't hang on to claim their first victory in Dingwall this season.
The home side made only one change from the side from the side that defeated Dundee United in their previous fixture, with Martin Scott starting in place of Rocco Quinn.
Neil Lennon once again rang the changes with the Scottish Cup final on May 26 against Hibernian the Hoops' only meaningful upcoming fixture, so Fraser Forster, Charlie Mulgrew, Thomas Rogne, Tom Rogic, Beram Kayal, Georgios Samaras and Gary Hooper all dropped out.
The SPL champions opened the scoring within four minutes after a poor pass back by Andre Hainault handed Celtic a corner, from which Kris Commons curled into the box for Stokes, who spun and slammed the ball beyond Michael Fraser in the Ross County goal.
The Irish striker had a chance to add to the Celtic lead with a free-kick from the edge of the area, but he was twice denied by the Staggies defence as they blocked both of his efforts at goal before eventually clearing.
Celtic continued to push forward, this time with two of the club's younger players linking up, as Dylan McGeouch played through Tony Watt on the left-hand side only the 19-year-old to see his shot saved by Fraser.
Midway through the first half, Derek Adams side finally made Celtic's stand-in goalkeeper Lukasz Zaluska work as Vigurs curled a free-kick from the edge of the area towards goal, but the Polish stopper saved comfortably.
Ross County got back level with five minutes remaining in the first half as Richard Brittain cut a free-kick back to Vigurs on the edge of the area and the midfielder unleashed a stunning effort that found its way to the top corner of the net.
Celtic hit back immediately but were denied a goal when Watt stroked home a McGeouch cross from the right wing only to be ruled offside by the assistant referee.
The Glasgow giants almost went ahead just before the hour mark as Efe Ambrose headed a Commons corner towards goal, but unfortunately for the Nigerian defender, his effort was hacked off the line.
The Highland side then had an effort of their own four minutes later, as Ivan Sproule manage to find space on the left and found the head of Steffen Wohlfarth, but the German striker couldn’t direct his effort on target.
With quarter of an hour left Ross County threatened again as Evangelos Ikonomou whipped in a cross from the left-hand side, but Wohlfarth couldn't get on the end of the ball from the Greek defender.
Both sides ultimately were forced to settle for the point which leaves the Dingwall club four points behind their Highland neighbours in the quest for European football.