In a desperate opening half hour where chances were few and far between, Laryea Kingston may have done better than direct an effort straight into the hands of Mike Fraser when at least two of his team-mates were better placed.
Caley Thistle replied with a Ross Tokely header and a shot from Don Cowie, but neither seriously troubled Steve Banks.
The best chances came in the last 15 minutes and, after captain Grant Munro had spurned a wonderful opportunity to give the hosts the lead, Hearts went in front on 34 minutes.
A surging run from left-back Lee Wallace caused panic in the Caley Thistle rearguard and despite Munro's well-timed block, Andrew Driver's cut back from the rebound was turned into his own net by Ian Black.
The visitors continued to look dangerous on the break and Andrius Ksanavicius forced Fraser into a smart save at his near post following a low shot from the edge of the box.
Despite falling behind, Caley Thistle could have gone in at the interval level when Marius Niculae headed the ball back across goal, but Christophe Berra managed to clear the danger with Dennis Wyness lurking.
Inverness continued to ask questions of the Hearts defence and after the half-time interval Wyness was unlucky with a header that drifted inches past.
It did not appear as if it was going to be Caley Thistle's day once more as Berra blocked a shot from eight yards by Wyness, but they deservedly equalised on 64 minutes.
Not for the first time, Tokely found himself well inside the Hearts half and his weighted cross to the back post was fired goalwards by Barry Wilson.
Banks did well to block the initial effort but could do nothing to prevent Wyness from poking the loose ball over the line.
The visitors tried to rally with the industrious Kingston unfortunate to see a free-kick rebound to safety via the upright, before their misery was compounded as Alan Morgan crossed for Brewster in injury-time to volley home the winner.