Neil McCann tasted defeat for the first time since taking over as interim Dundee manager on a desperately disappointing night for the home side at Dens.
Ahead of the game, all the pressure was off Dundee with their Premiership survival confirmed on Tuesday night after Hamilton were beaten at Ross County.
In contrast, Inverness were drinking at the last-chance saloon knowing that defeat would consign them to automatic relegation.
However, it was the basement battlers who stormed into an early lead through goals by Billy Mckay and Alex Fisher.
McCann’s men manfully tried to get back into the game but it was Caley who held on to keep alive hopes of making a great escape.
The Dundee boss made just one change from the side that drew with Ross County at Dens on Saturday with Nick Ross coming in for Tom Hateley who had failed to recover from a dead leg and dropped out of the squad.
Dundee had a huge let-off with just one minute on the clock when keeper Scott Bain hammered an attempted clearance off Mckay with the goalie mightily relieved to see the ball flying back past his post.
However, just a minute later, Mckay was teed up inside the Dundee box by Liam Polworth and fired a low shot into the left-hand corner of Bain’s net to give Inverness a shock lead.
That shock doubled in the 10th minute when Iain Vigurs dinked a ball over the top to Fisher 14 yards out from Bain’s goal. The Inverness player controlled the ball with his head before sending a superb volley past the stunned keeper.
Dundee looked to respond and had a great chance in the 20th minute when Kevin Holt swung a corner in from the right with skipper Darren O’Dea finding room for himself but he headed wide.
Mark O’Hara then had a pop for the home side from 30 yards but his fizzing strike flew straight into the grateful arms of Caley keeper Ryan Esson.
Shortly after, O’Dea had another opportunity from a Holt corner but again could not direct his header on target.
The Dark Blues continued to press and just before the half-hour mark, O’Hara played in the overlapping Cammy Kerr down the right in a promising position but the full-back’s shot flew wide.
However, it was the home side who had another big scare when Brad McKay played a tempting cross from the right with Fisher heading just inches past Bain’s left-hand post.
The Dark Blues were next to threaten in the 41st minute when Faissal El Bakhtaoui played a pass to Ross who superbly flicked the ball into the path of Marcus Haber but Esson raced from his line to snuff out the danger.
McCann made a change at half-time with Daniel Higgins coming on for centre-half Kevin Gomis.
Dundee had a half chance in the 52nd minute when El Bakhtaoui played a long ball through to Haber but he headed well over with the big Canadian subbed shortly after.
As the hour mark approached, Caley looked comfortable with the Dark Blues struggling to make any sort of meaningful impact.
They did though fashion a chance when El Bakhtaoui played a cross in from the left towards O’Hara in a dangerous position but his glancing header was easily gathered by Esson.
In the 78th minute, Inverness had an opportunity of their own when McKay latched onto a corner from the right but his powerful header flew straight to Bain.
As the clock ticked down, Dundee’s effort to pry open the Caley defence became ever more desperate to the obvious frustration of the vast majority of the crowd inside Dens.
A brief period of pressure with four minutes to go ended with Kerr sending an attempted cross well wide of his intended targets which just about summed up the disappointing nature of the Dundee display.
Inverness sub Henri Anier then had a half chance to make it three but he could not make a firm contact.
However, his side’s two early goals were what ultimately counted with Inverness hanging on to take all three points.
Attendance – 5,574.
Dundee – Bain, Holt, Vincent, O’Dea, O’Hara, Ross, McGowan, El Bakhtaoui (Wighton, 72), Haber (Ojamaa, 55), Kerr, Gomis (Higgins, 45).
Subs not used – Ferrie, Dryden, Williams, Smith.
Inverness – Esson, Raven, Warren, Polworth, Draper, Vigurs (McCart, 89), Mckay (Anier, 66), Tansey, Fisher (McNaughton, 85), Laing, McKay.
Subs not used – Hoban, Mulraney, Ebbe, Cole.
Referee – Kevin Clancy.