A Billy McKay double propelled Inverness to a 4-1 win and left Dundee still searching for a first home point of the Clydesdale Bank Premier League season.
McKay put Caley Thistle in front after four minutes and Gary Warren doubled the lead two minutes later as the visitors appeared set to extend their unbeaten run to six at Dens Park.
Colin Nish pulled a goal back after 13 minutes, but Andrew Shinnie converted an 81st-minute penalty before laying on McKay's second as Terry Butcher's men climbed to third place in the standings.
Dundee boss Barry Smith welcomed Friday night football, but he may have wished for a quiet night in after his side made a dreadful start.
Nicky Riley, one of four changes for the hosts following the loss to Hibernian, flashed a shot wide, but 30 seconds later the hosts were behind.
Dundee delayed too long on the ball at the back and Neil McGregor's clearance was blocked. The ball fell for Aaron Doran, whose shot was parried by Rab Douglas, leaving a simple tap-in for McKay, in for injured captain Richie Foran.
The shell-shocked hosts found themselves two down little more than a minute later. Again Doran was the provider, his free-kick from the left finding Warren to net from close range.
Riley blasted off target from an angle before the deficit was halved when Nish drilled a loose ball low under Antonio Reguero after Steven Milne's shot was blocked. Doran continued to trouble Dundee down the right, with the hosts doing little to aid their cause by relinquishing possession all too easily.
Shane Sutherland, who replaced Roberts after 64 minutes, crossed from the right to find Draper, whose first-time shot ricocheted down off the crossbar. Sutherland was felled by a rash Iain Davidson challenge and Andrew Shinnie converted from the spot nine minutes from time.
Inverness struck again with five minutes remaining as Andrew Shinnie turned provider. The playmaker ran at the heart of the Dundee defence and found McKay, who was composed enough to take his time before firing past Douglas to seal victory.