Caley Jags manager John Hughes made two changes to the side which lost at Partick Thistle before the international break with Danny Devine and Danny Williams dropping out, Nick Ross and Aaron Doran taking their places in the starting 11.
Hughes also reverted to his 4-2-3-1 formation for the visit of Paul Hartley’s side and it resulted in a controlled and commanding display from the Highlanders.
Home goalkeeper Ryan Esson was a virtual spectator in the first half as he watched all the action unfold in the Dundee half.
His Dark Blues counterpart Scott Bain, however, was kept busy by Caley Jags as he had to contend with several long range efforts from Greg Tansey and Doran.
But the former Alloa goalkeeper dealt comfortably with the shots from the Inverness duo to ensure the game remained goalless at the break.
Dundee had to improve and they did just that in the second half with David Clarkson putting the visitors ahead with his side’s first shot on goal.
The loss of the goal spurred the home side into action and captain Graeme Shinnie hit back immediately with an angled drive past Bain to make it 1-1.
Inverness pushed for a winner and Edward Ofere was clean through but could not get his chip over Bain on target, leaving the home side having to settle for a point.