Vigurs found the top corner from 20 yards following a set-piece four minutes before half-time to cancel out Anthony Stokes' early opener as the clash finished 1-1.
But Celtic should have gone into the break with a deserved lead after Tony Watt was denied a goal by a dubious offside decision.
County recovered from two down to beat Celtic 3-2 in their previous meeting and they again improved as the game progressed but could not get the winner they were pushing for to boost their hopes of a European place.
The draw means they are now four points adrift of third-placed Inverness in the Clydesdale Bank Premier League and Caley Thistle will put County out of the running for a Europa League spot before the final-day Highland derby if they beat Dundee United at home on Saturday.
Celtic manager Neil Lennon again made a number of changes after resting players for last weekend's 3-1 defeat by Motherwell with the title already won.
Efe Ambrose, Kelvin Wilson, Kris Commons and Joe Ledley returned following their holiday while Rami Gershon was handed a rare start and Lukasz Zaluska and Dylan McGeouch also came in.
Fraser Forster was rested and Georgios Samaras, Gary Hooper, Charlie Mulgrew were given this week off by Lennon while Victor Wanyama was also absent.
There was something of a false start to the game when the ball failed to re-emerge from the away fans after Celtic's first attack but the visiting team were in no mood to waste time and Stokes opened the scoring with just over three minutes on the clock.
County failed to deal with Kris Commons' inswinging corner as it bounced inside the six-yard box and the Irishman had time to chest the ball down before turning and firing into the net.
Celtic were causing County problems down the wide areas with their 4-3-3 formation with centre-forward Stokes peeling off to good effect and Michael Fraser had to be alert to push away Watt's ball across the face of goal.
The hosts were unable to string together a meaningful attacking move until midway through the half when Martin Scott got a shot on target but Zaluska got down to hold.
The Pole made a better save two minutes later when he dived to push away a Vigurs free-kick that was destined for the top corner.
Celtic were soon back on the attack and Stokes' clever ball across the six-yard box deserved a more alert response from Watt.
The visitors were comfortable but they were caught out in the 41st minute because of some slack marking and a wonderful finish from Vigurs.
Vigurs was left all alone as Richard Brittain lined up a free-kick after Ambrose had fouled Ivan Sproule just outside the left edge of the penalty area and the talented midfielder side-footed the ball into the top corner from 20 yards.
Celtic should have been back in front when Watt netted with the last kick of the half but assistant referee Dougie Potter flagged for an offside decision.
Watt appeared to be played onside by Hainault before he diverted home McGeouch's driven pass after Ambrose, playing in midfield, had launched an attack.
Celtic had the first chances of the second half. Fraser pushed a 25-yard drive from Stokes wide and Brittain stretched to clear Ambrose's header off the line following a Commons corner.
But Ross County were enjoying a better share of the play in the second half with the wind at their backs and Steffen Wohlfarth headed just past the top corner from Sproule's cross before failing to connect with an inviting centre from Evangelos Oikonomou six yards out.
Some slack defending from Gershon twice almost allowed Sproule to punish the visitors and Paul Lawson twice came close from long range.
Celtic had lost their spark after Commons went off for Tomas Rogic and they brought on Paddy McCourt with seven minutes left but could not create a late chance.
- Sports & Recreation
- Anthony Stokes
- Kris Commons
- Tony Watt