Both sides remained unchanged from their opening-day matches, but it was Dundee having to juggle their first team on just eight minutes when injured captain Kevin Thomson was replaced with Jim McAlister.
Caley midfielder Ross Draper had the first meaningful effort of the game, launching a stunning 45-yard lob that floated just over Kyle Letheren’s crossbar.
With Caley Thistle, eyeing their second win of the season, again deploying a more patient approach, supporters had to wait for half an hour to see a decent chance as Billy McKay picked up the ball from Ryan Christie before drilling a low left-foot strike straight at Letheren.
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.
Inverness maintained their dominance after the break and came close to taking the lead, only for a last-ditch challenge from James McPake denying the lively McKay.
Inverness continued to threaten as Draper headed a Christie free-kick straight at Letheren, but it was time for the visitors to show some late spirit, only for substitute Peter MacDonald to blaze over Gary Harkins’ corner.
Harkins was proving to be quite a menace and only David Raven’s saving tackle prevented Dundee from taking a shock lead.
Former Hereford man Marley Watkins had the final chance to break the deadlock for the hosts but his effort was blocked as both teams had to settle for a point.