County moved a point closer to Scottish Premiership safety, but this must go down as a missed opportunity.
The Staggies fell behind after only three minutes to a sublime goal from Italian midfielder Massimo Donati, but the match swung back in their favour on the stroke of half-time when Accies defender Ioannis Skondras was sent off for a late challenge on Ryan Dow.
Craig Curran restored parity in the 60th minute with his seventh goal of the campaign and it looked as if momentum was with the Staggies to go on and claim all three points.
But they could find no way past the well-organised 10 men and were fortunate to avoid leaving with nothing with Martin Canning’s side passing up two opportunities.
The result moves the Dingwall side seven points clear of bottom of the league Caley Thistle and three ahead of Motherwell, who currently occupy the relegation play-off place.
A victory would have moved County up to seventh spot but it was hard to begrudge the industrious Accies a share.
County still have work to do to ensure they will be playing in the top flight next season.
A 2-1 victory against Dundee on Tuesday, sealed by a last-minute Liam Boyce penalty, had lifted some of the pressure after a solitary win in nine matches had sucked them into relegation danger.
Saturday’s match was a chance to open more breathing space ahead the Accies who started the day in the relegation play-off place and only three points above Caley Thistle.
The Staggies, who had lost only one of their previous seven top-flight encounters against Accies, made one enforced change with Dow stepping in for the suspended Jim O’Brien.
Accies had reduced tickets to £10 in a bid to get as many supporters in New Douglas Park for a crucial game with free entry for under-16s – but only a crowd of 1,548 turned up to enjoy a day of football in the sunshine.
For those who could be bothered this was a highly entertaining spectacle from the off.
County had men in the right place to make a goal-line clearance and deny Alex D’Acol but Accies got in front after only three minutes thanks to a majestic finish from Donati who found the top corner from 20 yards.
County almost equalised immediately when Dow crossed for the unmarked Tim Chow, but the midfielder blazed over from only six yards out.
There were still only eight minutes on the clock when Scott Fox made a terrific save to keep out a D’Acol drive that looked destined for the top corner.
It was breathless stuff and Michael Gardyne was unfortunate not to get on the scoresheet with a well-struck attempt that flashed inches wide.
Then a moment of controversy in first-half injury time when Skondras was shown a red card for a late challenge on Dow as he advanced.
It looked to be wild and reckless from the Greek right back and the correct decision from referee Steven McLean.
Post-match McIntyre, with the aid of having seen the incident again, admitted the referee got the game’s major decision wrong.
With a one-man advantage, the onus was on County to make it count and they almost equalised in the 58th minute when Dow, County’s best player, smashed the crossbar with a superb effort from the edge of the area.
They finally got back on level terms two minutes later when Curran scrambled the ball home from a Woods corner.
It was expected the Staggies would push for the winner in a rousing finale, but instead it was the 10 men of Accies who ended the game strongly.
Scott McMann stormed past two County players before eventually being denied by Fox in one nervy moment for the visitors before Accies passed up an even better chance deep into added time when Dougie Imrie squared the ball to substitute Alex Gogic who shot over with the goal at his mercy.
