Hamilton have been sent closer to the play-off after Billy McKay's last-gasp strike earned Inverness a first win over Accies this season.
Connor Smith's terrific free kick looked like giving them an amazing fifth straight win over their Highland visitors, but that lasted only three minutes before Nathan Shaw levelled.
And McKay popped up with a late winner to break Hamilton's hearts, with Cove due to play Arbroath on Saturday while Accies host Partick Thistle in their penultimate game.
Inverness were on a five-game winning streak and were clearly the more confident side, dominating much of the game at New Douglas Park.
It was the one flash of actual brilliance from Smith, who in the first half curled an exquisite shot round the top right corner with goalkeeper Mark Ridgers a helpless spectator.
But Hamilton's poor defending came back to bite them again as Shaw ghosted in at the right post to smash in Danny MacKay's cross.
And McKay's strike earned them a first win in five over Hamilton.
A goal-less first half was dominated by Inverness, who forced a couple of good saves from Accies keeper Ryan Fulton, while Hamilton created some half-chances, but never really troubled Mark Ridgers.
The closest Accies came was when Connor Smith curled a brilliant shot just round the top right corner.
In the second half it was much more even, with both sides trading chances before Smith's opener.
Accies head coach John Rankin made two changes from the side that lost 1-0 at Queen's Park last Friday night. Reegan Mimnaugh and Jean-Pierre Tiehi came in for Lucas de Bolle and Andy Winter.
Lewis Spence was on the bench, as he continued his rehabilitation from a serious knee injury.
Inverness boss Billy Dodds made three changes from the team that beat Cove Rangers 2-1 on Saturday. Robbie Deas, Aaron Doran and ex-Accies kid Stevie Boyd came in for Cameron Harper, Austin Samuels and Danny MacKay.
Inverness created the first chance inside a minute when David Carson was sent down the right but his low cross flew across the face of goal with no takers.
Billy McKay had a shot parried in four minutes as the visitors threatened again.
A defensive howler allowed Aaron Dorans to get the bounce of the ball in nine minutes but his lay-off to McKay was well cut out by Dan O'Reilly.
Accies were given another let-off in 13 minutes when a sweeping move ended with Zak Delaney firing over from the left side of the box.
Delaney's dipping corner from the right was punched out by Ryan Fulton at the far post corner in 16 minutes.
Inverness should have taken the lead in 19 minutes when Dylan McGowan was short with a pass-back and that let in McKay, but he could only find the left side-netting.
Mimnaugh had a go for Accies from 20 yards in 23 minutes, but it landed wide of the right post.
Connor Smith let fly with a curling shot that flew just past the top right corner in 28 minutes.
Boyd picked out Nathan Shaw in 30 minutes, but Steve Lawson got a foot in to clear, at the expense of a corner, which came to nothing.
Robbie Deas nearly scored from Delaney's corner on the right, but Fulton superbly saved his header at the back post.
Inverness should have taken the lead in 49 minutes when Delaney broke down the left and cut he ball back for Doran, but his shot was deflected past the left post.
Sean Welsh fired a 20-yard free kick over in 55 minutes as the visitor continued to threaten.
At the other end, Benny Ashley-Seal had a low shot saved by Ridgers' foot.
Doran sent an angled shot inches past the left post in 58 minutes as the sides traded chances.
Boyd sent a low effort wide of the right post from 25 yards in 64 minutes.
McKay tore down the left flank in 70 minutes and his cut-back picked out Boyd, but he could only find the right side-net.
Accies took the lead in 71 minutes when Connor Smith curled an unstoppable free kick into the top left corner.
But Inverness levelled three minutes later when Danny MacKay's cross was smashed in at the right post by Shaw.
Sub Dario Zanatta sent a shot whistling past the top right corner from the left wing in 77 minutes.
It looked like ending all square, before McKay popped up with a late winner for Inverness, latching onto Welsh's through-ball.
HAMILTON: Fulton, Sparrow, McGowan, Reilly, Tumilty (Winter, 68), Lawson, Mimnaugh (de Bolle, 62), Martin, C. Smith, Tiehi (Zanatta, 68), Ashley-Seal.
Subs (not used): J. Smith (GK), Easton, Spence, L. Smith, Stephenson, McGinn.
Booked: Martin (44), O'Reilly (59)
INVERNESS: Ridgers, Carson, Devine, Delaney, Deas, Doran (Samuels, 72), Allardice, Welsh (Harper, 89), Boyd (MacKay, 72), Shaw, Mckay (Woods, 89).
Subs (not used): Mackay (GK), Hyde, Nicolson.
Booked: Devine (24)
Referee: Graham Grainger.
Attendance: 1316
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