A penalty save by the Inverness goalkeeper Owain Fon Williams denied Hearts victory against the Scottish Premiership's bottom club.
Jamie Walker's spot-kick was expertly saved by the Welshman low to his left 15 minutes from the end of the 1-1 draw at Tynecastle.
Carl Tremarco headed the Highlanders into a deserved first-half lead, but Arnaud Djoum levelled for Hearts after the interval. Despite increasing pressure on the visitors' goal as the game progressed, those in maroon couldn't force a winner. They now head into Wednesday's Scottish Cup replay with Hibs at Easter Road harbouring a good deal of frustration.
Walker didn't start the match having been rested and the game took time to ignite on a well-documented threadbare Tynecastle surface. It was Inverness who came to life first. Tremarco rose unchallenged inside the Hearts penalty box to head Greg Tansey's free-kick into the net on 24 minutes. That gave the league's bottom side something to fight for.
Tremarco made a vital block to prevent Arnaud Djoum equalising at the opposite end five minutes later. Bjorn Johnsen then struck the crossbar with a deflected effort after an incisive attacking run by captain Perry Kitchen, restored to the Hearts starting line-up by head coach Ian Cathro.
Fon Williams was airborne to tip Andraz Struna's 25-yarder for a corner as the hosts increased the pressure in search of parity. They reached the interval still seeking to break through the rigid Highland rearguard - in which centre-back Louis Laing was enjoying an assured debut.
From the most acute angle, Esmael Goncalves volleyed Choulay's cross against the inside of Fon Williams' right post early in the second half. The Moroccan winger was making his first start since agreeing a loan move from Stoke City and looked a useful attacking outlet.
Inverness were clearly determined to protect their advantage and took every opportunity to break up the play. Hearts introduced Walker and Rory Currie hoping for some fresh invention. On 64 minutes, they forced an equaliser. Kitchen justified his reinstatement to the team by delivering a cross from the left which Djoum tapped into the net at the back post.
The cheers around Gorgie were more of relief than outright joy. There were a few more puffed cheeks moments later when Caley Thistle's lone forward Billy Mckay missed a glaring chance to restore his team's lead from a corner. Clearly, Hearts had much work to do in the remaining 25 minutes.
Again Inverness hit the post when Ross Draper's header from a corner was allowed to bounce across goal and strike the upright before being hoisted clear. Then came the opportunity Hearts had waited for when they were awarded a penalty. Djoum was bundled over by Draper inside the box, but Walker's spot-kick was superbly saved by Fon Williams low to his left.
The goalkeeper stopped shots from Walker, Currie and their fellow substitute Malaury Martin towards the end - thus ensuring Inverness prised a welcome result from this trip to the Capital.
Hearts (4-4-1-1): Hamilton; Struna, Avlonitis, Hughes, Sowah; Djoum, Kitchen, Tziolis, Choulay; Johnsen, Goncalves.
50: Walker for Johnsen
62: Currie for Choulay
76: Martin for Kitchen
Unused subs: Noring, Nowak, L Smith, Nicholson.
Inverness CT (4-1-4-1): Fon Williams; Raven, Laing, McCart, Tremarco; Draper; Mulraney, Tansey, Polworth, Cole; Mckay.
62: Doran for Mulraney
80: Anier for Mckay
Unused subs: Hoban, Ebbe, Fisher, Boden, Gilchrist.
Referee: Bobby Madden.