Caley striker Adam Rooney's late spot-kick meant a share of the spoils at Easter Road on Saturday.
Riordan put Hibs ahead in the eighth minute as they began life without Anthony Stokes in encouraging fashion, but the striker was made to rue a 66th-minute penalty miss as battling Inverness claimed a SPL point.
Terry Butcher's side had already hit the woodwork through Rooney, before the striker made no mistake with his spot-kick eight minutes from time to snatch a draw in an entertaining game.
John Hughes' men saw their winless streak at home stretch to eight games and were booed off at the finish.
Hughes made four alterations from the side defeated by St Mirren.
Out went Stokes, now at Celtic, with captain Chris Hogg, Ian Murray and Steven Thicot all benched.
Michael Hart and Kevin McBride were restored with new signings Jonathan Grounds and Francis Dickoh handed their debuts.
Butcher rang two changes from the team that lost to Hamilton. Russell Duncan and on-loan Kevin McCann, ineligible against his own side, missed out with Ross Tokely and new signing Stuart Duff brought in.
The visitors began positively, enjoying possession, but Hibs broke upfield to register the first shot as Riordan skewed wide.
Inverness responded with a Jonny Hayes corner that David Proctor headed over.
The hosts, though, were finding their feet and in the sixth minute Edwin de Graaf played in Riordan who looked set to round Ryan Esson before the goalkeeper brilliantly clawed the ball away from the striker.
However, on eight minutes, it was to prove third time lucky for Riordan as he grabbed his first goal of the season.
Grounds and David Wotherspoon combined well on the left and the ball broke to Colin Nish on the 18-yard line.
The forward quickly fed his partner Riordan, who nutmegged Grant Munro, before drilling the ball low across Esson and into the right-hand corner.
The Highlanders regrouped and Hayes' free-kick was nodded wide by Munro.
The dangerous Hayes then held off Grounds on the right flank before striking the side-netting.
As the contest ebbed and flowed, Wotherspoon tried his luck from 20 yards and curled just wide.
Riordan then scampered down the right flank to collect a loose ball, squaring for Nish who saw his effort deflected wide.
Butcher's side were still very much in the match and, six minutes from half-time, their big chance came.
Eric Odhiambo cut back from the by-line and Rooney seemed destined to score from six yards, only for Brown to make a point-blank stop from his shot. Inverness made a change at the break, Chris Innes replacing Kenny Gillet.
Riordan soon went close to doubling the advantage, his free-kick arcing for the top left-hand corner only for Esson to palm over.
But Caley Thistle, 2-1 winners on their last visit to Easter Road in November 2008, came within inches of levelling matters in the 55th minute.
Nick Ross' reverse pass put Rooney away on the left flank and his fierce angled strike looked net-bound until it smacked back off the top of the near post.
Inverness had their tails up and only an overhit Rooney pass prevented Odhiambo racing clear on goal, before Brown dropped a Tokely cross and Hayes couldn't capitalise.
Hibs, though, should have been two ahead two minutes after the hour.
Liam Miller played a central pass through to Nish who was brilliantly blocked out by Esson. The ball broke to De Graaf but somehow the Dutchman blazed over an open goal from eight yards.
Hibs quickly passed up another glorious chance when Proctor clipped Riordan in the area and referee Crawford Allan pointed for a penalty.
Riordan dusted himself down but struck the right-hand post with his spot-kick.
A rash of substitutes interrupted play and it was two replacements who were at the centre of Inverness' 82nd-minute equaliser.
Thicot, on for Hart at right-back, clipped the on-rushing Inverness sub Danni Sanchez and Rooney was handed the task from the penalty spot.
The Irishman made no mistake as he lashed past a despairing Brown.
Hayes then whipped in a great cross that another Inverness sub, Shane Sutherland, knocked over with the goal gaping.
Hibs thought they had won it three minutes into stoppage time but Wotherspoon was flagged offside after netting.