Inverness dominated the opening period of the game before Tudur Jones put them into the lead after 19 minutes.
Andrew Shinnie did well before passing the ball to the 28-year-old, who fired the ball into the top corner from the edge of the penalty area.
That appeared to be the catalyst for Hearts to become more involved in the match as Ryan Stevenson quickly saw a shot saved.
Hearts began to press for an equaliser at the start of the second half and Marius Zaliukas and Stevenson both saw efforts blocked.
Jason Holt was the next Hearts player to try his luck but he saw his long-range effort drift harmlessly over the crossbar.
Zaliukas broke clear of the Inverness defence with five minutes remaining but he could not direct his shot on target.
However, redeemed himself in injury time when he converted a penalty after Tudur Jones brought down Paterson in the penalty area.