Neither side could claim to deserve the three points at the Caledonian Stadium and a sharing of the spoils from a goalless draw was inevitable.
Both sides remained unchanged from their respective opening-day matches. Inverness striker Billy McKay - amid reported interest from German side FSV Frankfurt - retained his place up front as he sought to add to his goal against Hamilton.
But Dundee were dealt a blow after just eight minutes when they were forced to replace their injured captain, Kevin Thomson, with Jim McAlister.
Caley midfielder Ross Draper had the first meaningful effort of the game, launching an audacious 45-yard lob that floated just over Kyle Letheren's crossbar.
Greg Stewart was the first to test Dean Brill as he headed Paul McGinn's cross straight at the Inverness goalkeeper, before a neat passing move from the hosts resulted in Letheren claiming David Raven's near-post cross.
The next chance for the visitors came in similar fashion as Stewart stood the ball up for McAlister, who headed low and straight at Brill.
With Caley Thistle again deploying a more patient approach with the ball, supporters had to wait until the 35th minute to see another clear opportunity.
Ryan Christie laid off McKay, who was drifting between his striker role and the right wing, drilled a low left-foot strike straight at Letheren.
A quick break very nearly opened the scoring, and it was McKay who was tearing away from the Dundee defence.
He squared to Christie on the left-hand side of the area but, instead of laying off Danny Williams, tried to make space for himself and saw his effort blocked.
The second half began with Inverness once again controlling position but lacking penetration behind the Dundee defence.
James Vincent lasted justed five minutes of the second period, being replacing by former Hereford man Marley Watkins.
Their first chance of the second period came just before the hour mark and only a last-ditch challenge from James McPake denied Caley Thistle the lead.
Graeme Shinnie fed Watkins on the edge of the area and he played a one-touch pass to Williams.
His drilled cross would have been turned in by McKay but for a late intervention by the former Hibernian defender.
It was the left-back who threatened the Dundee goal on 70 minutes after being played in by Christie.
Shinnie hammered the ball at Letheren and the goalkeeper saved, only for the captain to scoop the follow-up high over the crossbar.
Inverness did threaten from a set piece as the game entered the final 15 minutes, Draper heading a Christie free-kick straight at Letheren with Gary Warren waiting to power home.
The visitors missed a glorious opportunity to punish Caley Thistle with a set piece of their own.
Gary Harkins' corner made it all the way to the back post for Peter MacDonald, but the substitute only succeeded in finding the stand behind the goal.
Harkins came even close just moments later when Dundee caught Inverness on the break, being denied only by David Raven's saving tackle.
Watkins' late break represented the closest Caley Thistle came to a winning goal but his goal-bound effort was blocked.