The result did the Jambos no favours with Rangers winning in the chase for second place, but it does keep Caley Thistle in the top six.
Rudi Skacel, Edgaras Jankauskas and skipper Steven Pressley were all sidelined for the Jambos, who did at least have midfield ace Paul Hartley back in the side.
Dennis Wyness, on loan from Hearts until his contract kicks in this summer, sat this one out as part of the gentleman's agreement between the clubs and Graham Bayne stepped into his place.
Barry Wilson had not fully recovered from his ligament surgery to stake a claim and Alan Morgan filled in, while young forward Rory McAllister was suspended.
Inverness were trying to earn the three points that would keep them ahead of rivals for sixth spot, Aberdeen and Motherwell, while Hearts were desperate to win to stay ahead of Rangers and Hibs for that sought-after Champions League spot.
In the opening moments, a Russell Duncan 30-yarder and a Takis Fyssas header caused either defence a moments trouble.
A slack piece of defending from Richard Hastings led to Hearts' Roman Bednar racing through on goal on eight minutes, but Mark Brown was equal to his shot.
Bednar was looking in fine form and his 29th minute shot after another Hastings error ended when Brown dived and held the low effort.
Then, at the other end, a Richie Hart speculative shot from the edge of the area was grasped gratefully by keeper Craig Gordon.
And he was at it again seconds later with a swerving drive that tested the Scotland number one.
It was the Inverness men probably felt they should have been in front by the break, but they started well in the opening exchanges in the second half and Hart tested that man Gordon again with a well-placed free-kick from fully 25 yards.
Two Bayne headers almost made the difference as the Highlanders pressed for the winner. However, time ran out on both sides and they had to settle for a share of the spoils.