Jamie Walker put the home side ahead as he burst into the penalty box, shook off his markers and rounded goalkeeper Owain Fon Williams.
Abiola Dauda doubled the advantage after the break when he pounced on a poor Greg Tansey pass back.
It was Hearts' first win over Caley Thistle in 12 meetings since 2011.
Hearts had given 19-year-old Liam Smith his first league start after the news that right-back Callum Paterson would be out for about a month with a shoulder injury.
The home side started brightly, but Jordan Roberts connected with a Danny Williams cross at the other end, only to head straight at the feet of Neil Alexander in the Hearts goal.
Roberts created another opportunity when he got the better of Igor Rossi on the left but fired his effort wide of goal.
Hearts began to dominate the midfield area, with Arnaud Djoum and Prince Buaben looking to play in wingers Sam Nicholson and Walker at every opportunity.
Smith came close to what would have been a stunning opener, the teenager's sublime first touch taking him inside before he fired a left-foot shot just over the crossbar.
The breakthrough came 10 minutes before the break when Alim Ozturk played in Walker, who drifted in from the left and, despite the attentions of three Caley Thistle defenders, eased his way into the box before slotting the ball into the right-hand corner of the goal.
Hearts almost doubled their advantage before the break when Rossi's effort from 20 yards was just wide of the target.
The home side began the second half strongly and Dauda had already fired straight at goalkeeper Fon Williams before they went further ahead.
Tansey was only a few yards inside his own half as he tried a pass back to Fon Williams, but it was terribly short and Dauda raced past the stranded goalkeeper before rolling the ball into the empty net.
Caley Thistle tried to push more men forward, but that left the defence exposed and Dauda looked certain to score again, but his effort was weak.
The visitors came close to pulling one back when Iain Vigurs' 18-yard strike was pushed away by Alexander's low dive.
Caley Thistle did find the back of the net in stoppage time, when substitute Liam Hughes rounded Alexander to score, but the flag was up for offside.
Hearts moved to within six points of second placed Aberdeen in the Scottish Premiership with a comfortable win over Inverness Caledonian Thistle.