The Scottish champions had been aiming for 10 wins out of their opening 10 matches - what would have been their best start to a season for 112 years.
Maurice Edu provided a first-half lead, but substitute Eric Odhiambo came off the bench to snatch a late leveller as the Highlanders maintained their unbeaten run on the road in the league which stretches back almost a year.
Rangers made four changes from their midweek Co-operative Insurance Cup win at Kilmarnock for the visit of Inverness.
Kyle Lafferty and Sasa Papac were back from illness and injury respectively, while goalkeeper Allan McGregor and Kenny Miller were also added to the side.
Inverness made one change from their win over Kilmarnock in the SPL last week, with Kevin McCann replacing Odhiambo.
Rangers were the more dangerous team in the opening spell and could have taken the lead when Madjid Bougherra supplied a cross from the right for Edu in front of goal, but Ross Tokely managed to intercept and nod to safety before the American could connect with the header six yards out.
But Edu did leave the net bulging with 11 minutes on the clock when he collected a long ball from Steven Davis and lashed high into the top corner, leaving Ryan Esson helpless in the Inverness goal.
Miller then had a go as Rangers tried to double their advantage but this time Esson was up to the task and able to smother to deny the striker his 14th goal of the season.
Richie Foran picked up the first booking for a crunching tackle on Edu, who required treatment before being able to return to the action.
Rangers continued to press for a second goal and David Weir was not too far away with a header that fell just over the crossbar from a Vladimir Weiss corner.
Kirk Broadfoot then released Bougherra on a run down the right flank and the Algerian tried to slip into the path of Lafferty as he bore down on goal, but Tokely was alert again to snuff out the danger.
With Edu presumably struggling following the earlier challenge, he was withdrawn at half-time along with Weiss, and Steven Naismith and John Fleck were thrown into the action.
Rangers immediately set about trying to add to their scoreline and Davis dragged his shot an inch wide of the upright from just inside the box.
Inverness could have levelled had it not been for the heroics of Allan McGregor, when Foran's downward header bounced off the turf in front of the goalkeeper, who just managed to tip over the crossbar.
At the other end, Esson also pulled off an impressive save when, at full-stretch, he was able to punch a stinging effort from Fleck over.
Fleck turned provider when he whipped a corner into the box for Miller, but his header flashed across goal and wide as Rangers continued to pass up chances in front of goal.
They were left rueing those spurned opportunities when Inverness hauled themselves level with eight minutes to go. Foran's pass was collected by substitute Odhiambo, who stabbed past McGregor.
Rangers surged forward in search of the winner and Papac's cross found Bougherra at the back post, but he was denied by Esson as Inverness survived a late onslaught to earn a point.