Hearts substitute Michal Pospisil scored with his first touch to settle a dull encounter at Tynecastle.
Michal Pospisil was the goal-hero for Hearts
With eight minutes remaining, Andrew Driver's cross was expertly nodded home by the Czech striker.
Hearts again left out Craig Gordon but replacement goalkeeper Steve Banks made impressive saves to deny Graham Bayne and Barry Wilson in the first half.
The home side improved after the break, with Driver and Roman Bednar having chances before Pospisil's breakthrough.
Hearts started without Scotland goalkeeper Gordon for the fourth game in a row, with Lithuanian Eduardas Kurskis replacing him on the bench.
Elsewhere, Christos Karipidis, Lee Wallace, Neil McCann, Saulius Mikoliunas and Michal Pospisil were replaced by Takis Fyssas, Christophe Berra, Julien Brellier, Edgaras Jankauskas and Arkadiusz Klimek.
Inverness named the team which defeated Dundee United 1-0 in the Scottish Cup last weekend.
And the visitors were denied an early goal by the agility of Banks.
A long throw from Grant Munro was flicked on by Darren Dods and Bayne's volley from close range was wonderfully parried away by the English keeper.
Polish striker Klimek, making his Hearts debut, then drove a shot over the bar after a swift counter-attack.
Fyssas was busy in the opening exchanges with his fifth-minute cross just out of the reach of Jankauskas and his 18th-minute shot flashing across goal.
The Greek left-back then had his penalty claims waved away when he collapsed after stabbing the ball through the legs of Dods.
Steve Banks made two smart saves in the first half
Banks again came to the rescue of Hearts when he got down smartly to keep out a shot from Wilson.
The veteran midfielder, making his 300th appearance for the Highlanders, then drove a dangerous low ball across goal but Rory McAllister, at full-stretch, could not divert the ball home from inside the six yard box.
Klimek made a lively start to the second half but he made a mess of a chipped shot after a slip from Dods had given him a glimpse of goal.
Hearts winger Driver saw his volley flashed a yard wide as the home team upped the tempo.
Laryea Kingston then released Bednar with a neat pass but Inverness keeper Michael Fraser was quick off his line to block the substitute's strike.
Inverness were not seeing as much of the ball but a rare break forward saw a great looping header from McAllister clip the frame of the goal.
Pospisil was introduced for the final ten minutes and immediately made an impact, heading home a good delivery from Driver.
Inverness threw men forward in the closing stages but the home side held on to take maximum points.
Hearts: Banks, Tall, Zaliukas, Berra, Fyssas, Klimek (Pospisil 81), Kingston, Brellier, Driver, Jankauskas (Bednar 61), Elliot (Jonsson 73). Subs Not Used: Kurskis, McCann, Wallace, Karipidis.
Booked: Brellier. Goal: Pospisil 82.
Inverness CT: Fraser, Tokely, Dods, Munro, Hastings, Wilson (McSwegan 85), McBain, Duncan, Rankin (Morgan 63), Bayne, McAllister. Subs Not Used: Ridgers, McCaffrey, Black, Paatelainen, Soane.
Ref: E Smith