The Glasgow giants got off to the perfect start as 38-year-old Clint Hill capitalised on some poor defending to power home a header in the eighth minute.
However, County claimed an equaliser in the 26th minute when the unmarked Andrew Davies was allowed the freedom of the Rangerspenalty area to head past Wes Foderingham.
Neither side could add to their tally in the second half as Rangersdropped points for the seventh time in 12 league games since their return to the Scottish Premiership.
It leaves them in third trailing bitter rivals Celtic, who defeated Inverness Caledonian Thistle 3-0 on Saturday, by a massive 11 points with the leaders also having a game in hand.
Rangers manager Mark Warburton was deeply disappointed to watch his side draw for the fifth time this season.
"Our level of performance was nowhere near as good as last week's was (the 3-0 win over Kilmarnock) and we have to ask why," Warburton said.
"We must move the ball better and take care with our decision making."
Ross County manager Jim McIntyre was proud of his players.
"When you've been on a run like we've been on it can be difficult at times but I thought they showed their togetherness today," McIntyre said.
"We got into some good areas and if we had taken a bit more care with the final pass we might have hurt Rangers more than we did."
Hill -- who made his professional debut for Tranmere in 1997 -- rose high to get on the end of a Josh Windass corner and plant a header beyond Scott Fox into the far corner.
The visitors came close to adding another when Lee Wallace released Kenny Miller in the box but the veteran striker's shot was pushed into theside netting by the County 'keeper.
A second goal looked inevitable for Rangers but Ross Countyresponded in the 26th minute when some sloppy defending allowed them to grab only their tenth goal this season.
Davies was left unmarked at the back post which allowed him time and space to plant a bullet header past Foderingham from former Rangersplayer Chris Burke's corner.
Rangers dominated in the second period but were unable to profit from their possession and succession of corners.
They thought they had been awarded a penalty in the 67th minute when Jason Holt went down under Erik Cikos' challenge but instead referee Andrew Dallas booked the midfielder for simulation.
County finished strongly with Liam Boyce firing wide and substitute Tony Dingwall twice having shots blocked while Alex Schalk's late swerving effort was saved by Foderingham.
