Second-half goals from Gregory Tade and Stephen Elliott ensured a share of the points for Inverness and Hearts.
After a goalless first half, Tade was played in by Nick Ross following a mistake by Hearts' keeper Jamie MacDonald.
Tade hammered the ball past MacDonald, in goal for Hearts since replacing Marian Kello in the Edinburgh derby.
But Elliott levelled for the visitors, drilling home 10 minutes from time to secure a point.
Inverness started brightly with Graeme Shinnie and debutant David Davis combining well to set up captain Richie Foran for an early chance, only for him to be thwarted by a sliding Daniel Grainger tackle.
But both sides were cancelling each other out in the midfield with neither goalkeeper coming under any sort of pressure in the early stages.
Andy Webster would have opened the scoring for Hearts in 25 minutes if not for Shinnie stopping his shot on the line, following a Jamie Hamill corner.
That sparked the visitors into action with Elliott testing goalkeeper Ryan Esson after coming on to a Ryan Stevenson lay off.
Inverness fought back with brothers Graeme and Andrew Shinnie working together to set up Foran, whose header flew inches wide with neither side able to break the deadlock in the first half.
But the breakthrough did finally come shortly after the restart, MacDonald at fault when he slipped and gifted possession to Ross who set up Tade to hammer home his second goal of the season.
The Frenchman might have doubled the lead five minutes later when he latched onto an Andrew Shinnie through ball but MacDonald saved.
On the counter-attack Hearts substitute David Templeton hit the crossbar before Inverness hit back with Davis breaking down the wing before crossing in to Shinnie who sent the ball just wide.
Terry Butcher's side continued to dominate possession and looked likely to hold on for a win until 10 minutes from time.
The second-half introduction of Templeton and Mehdi Taouil proved to be inspired for Hearts, as both substitutes combined to play in Elliott.
The striker coolly slotted the ball home from inside the six-yard box, his shot squeezing in off the left-hand post past Esson.
There were late chances for Hearts to secure all three points, but the home side held out to ensure a third consecutive 1-1 draw between the sides.