Injury-hit Caley Thistle remain six points behind Championship leaders Ayr United thanks to their 2-2 draw against the front-runners.
Winger Nathan Shaw fired ICT ahead early on but Ayr hit back in the second half, with sub Mark McKenzie levelling.
Star forward Dipo Akinyemi’s seemed to have won it for United, but Shaw grabbed his second of the day to secure a deserved point.
Ayr are one point ahead of Morton and Dundee and two points in front of Queen’s Park, with ICT sixth in the division, behind Partick on goal difference.
It is now six successive games without a win for Caley Jags, but this show will give them encouragement.
Dodds made two changes to the side which lost 2-1 against Queen’s Park at Ochilview last week.
The surprise inclusion was the return of defender Danny Devine from injury, with Steven Boyd also starting. Zak Delaney missed out with a hamstring strain and George Oakley dropped to the bench.
ICT’s appeal to the SPFL to gain permission to bring players back from Highland League club didn’t pass in time for this match.
Lee Bullen’s Honest Men arrived in the north fresh from their 3-2 win at Hamilton eight days previously.
They also had the key weapon of 13-goal hitman Akinyemi, whose firepower is proving to be deadly this term.
The visitors made two changes from the Accies clash, with Daire O’Connor and Sam Ashford in for Jayden Mitchell-Lawson and Paul Smith.
Home keeper Cammy MacKay was called into action early on when he superbly pushed away a drive from Ashford.
However, the deadlock was broken on six minutes when a smart pass from Cammy Harper, who returned to left-back, led to Shaw rounding Charlie Albinson and tucked away his fourth goal of the season.
It was a positive start, with plenty of energy from the hosts who, despite their injury woes, had a spring in their step.
On 28 minutes, Aaron Doran was put through on goal and it took a full-on challenge from Albinson to halt his progress.
Chances were limited, but Inverness were the side on the front foot, looking most likely to find the net with their menace.
There was a moment of panic for the ICT support just before the break when a defensive Sean Welsh header flew over his own crossbar, a little too close for comfort. However, they went in one goal to the good at half-time.
Former Caley Jags loanee, Dundee United’s Logan Chalmers, created the first chance of the second half when he drew a save from Cammy MacKay just before Dipo Akinyemi flashed a shot just wide.
Inverness responded and Doran’s dipping drive just cleared the crossbar.
After soaking up Ayr pressure, ICT striker Billy Mckay then swerved a shot beyond the left post.
It was all square though on 66 minutes when, after a Chalmers run down the right, he cut it back for McKenzie, who buried it at the second attempt after Wallace Duffy blocked Akinyemi’s effort on the line.
Inverness won three corners on the spin after that but could not find an opening.
Doran then surged along the left touchline and his delivery was poked just wide by Boyd.
Ayr nudged in front with six minutes to go when Kirk’s header found Akinyemi and he coolly slotted the ball past Cammy MacKay.
It was a cruel blow for ICT, who had put so much into this contest and they blasted back as Shaw weaved forward, on to an Oakley ball, and knocked home the leveller with three minutes to go.
This was the least the Highlanders merited from a spirited performance and they keep the pack in front of them within range.
Inverness will now gear up for Scottish Cup third round action next weekend against League Two visitors Stirling Albion. Ayr will be in action two nights later when they host Pollok.
CALEY THISTLE (4-4-1-1) – Cammy MacKay 6, Duffy 6, Harper 7, Welsh 6, Devine 6 (Hyde 76), Carson 7, Billy Mckay 6, Doran 6, Ram 6, Shaw 7 (Oakley 83), Boyd 6. Subs not used – Ridgers (GK), Strachan, Calum MacKay, Nicolson.
AYR UNITED (4-3-3) – Albinson 6, Reading 6, McGinty 6, Kirk 6 (Ecrepont 90), McAllister 6, O’Connor 5 (Chalmers 44), Murdoch 6, Dempsey 6, Mullin 6 (Young 60), Ashford 6 (McKenzie 60), Akinyemi 6. Subs not used – McAdams (GK), Bilham, Bangala, Bryden, Smith.
Referee – Grant Irvine.
Attendance – 2066.
Man of the match – David Carson.
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