Hearts substitute Michal Pospisil scored with his first touch to settle a dull encounter at Tynecastle.
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.
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 Arkadiusz Klimek, making his Hearts debut, then drove a shot over the bar after a swift counter-attack.
Takis Fyssas was busy in the opening exchanges with his fifth-minute cross just out of the reach of Edgaras 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.
Banks again came to the rescue of Hearts when he got down smartly to keep out a shot from Barry Wilson. The veteran midfielder, making his 300th appearance for the Highlanders, then drove a low ball across goal but Rory McAllister, at full-stretch, could not divert it 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. Then Hearts winger Driver fired a volley a yard wide. Laryea Kingston then released Bednar with a neat pass but keeper Michael Fraser was quick off his line to block the substitute’s strike.
McAllister then went so close, his looping headerclipping 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 to no avail.
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.
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