Eighteen-year-old Conor Pepper rescued a draw for the Highlanders after they had appeared dead and buried at the break - two goals down and a man down following a tempestuous first period.
Arvydas Novikovas had given the hosts the lead on 15 minutes, curling past Ryan Esson, before John Sutton doubled Hearts' lead after a debatable penalty award.
Richie Foran was shown a red card on the stroke of half-time, prompting the fury of Terry Butcher, but Caley were handed a lifeline with a penalty of their own, Andrew Shinnie netting. Pepper then sparked wild celebrations among the visitors deep into injury time.
Novikovas was drafted in to replace David Templeton, serving the first of a two-match back for kicking Hibs captain James McPake.
Danny Grainger returned to the starting eleven, with young Kevin McHattie dropping to the bench, while Mehdi Taouil was charged with infusing the hosts with creativity, coming in for Scott Robinson. New signing Peter Enckelman had to be content ...