Eric Odhiambo gave Caley Thistle the lead in the 37th minute but a Chris Innes own goal on the stroke of half-time got the visitors back on level terms.
Ryan Stevenson then put Hearts ahead 10 minutes after the interval and Calum Elliot made sure of the points with the third goal 14 minutes later.
Caley Thistle made one change from the team that earned a point against Hibernian at Easter Road last weekend, with Innes replacing the injured Kenny Gillet, while there was a return on the bench for club captain Richie Foran, who was fit again after undergoing minor knee surgery at the beginning of the season.
Injury also deprived Inverness manager Terry Butcher of the services of on-loan Hibs defender Kevin McCann and Spanish forward Dani Sanchez.
As expected, new Hearts arrival Rudi Skacel was not involved in the squad due to not being fit as boss Jim Jefferies brought Elliot and Craig Thomson into the starting line-up with Kevin Kyle and Adrian Mrowiec dropping to the bench having started the 3-0 defeat to Celtic at Parkhead last Saturday.
Keen to make up for the disappointment for the loss to Celtic, Hearts began well in the rain-soaked Highland Capital, peppering the Caley Thistle penalty box with a number of crosses.
David Proctor’s attempted clearance cannoned off David Templeton and fell kindly into his path, but from a tight angle he fired the ball straight into Ryan Esson’s body.
Inverness had struggled to get out their own half, but a foul by Ruben Palazuelos on Jonny Hayes, for which the Hearts player was booked, presented the home side with a free-kick in a dangerous position.
Hayes took the set-piece and found the head of Adam Rooney, but his effort was easily held by Marian Kello.
The game then went into a little bit of a lull, although Caley Thistle came close to breaking the deadlock courtesy of another dangerous inswinging free-kick that was this time headed goalwards by Innes, but once again Kello was well positioned to stop the effort.
Stuart Duff was next to go into the referee’s book for a late challenge on Eggert Jonsson, while Ian Black failed to shake off a knock incurred from Rooney and the former Inverness player was replaced by Kyle.
Inverness were posing an increasing threat and they took the lead in the 37th minute. Nick Ross won possession of the ball on the halfway line and played it to Duff, who quickly found Odhiambo running through on goal. The forward took a touch to deceive Kello before sliding home the ball from close range.
Hearts, however, equalised right on the half-time whistle. Hayes brought down Templeton and was booked for his troubles. Templeton took the subsequent free-kick and delivered a dangerous ball that seemed to find the back of the net off Innes, although Kyle was in close attention.
Both sides pushed forward in search of goals at the start of the second half and only a timely intervention by Ismael Bouzid inside the six-yard box prevented Odhiambo from converting Rooney’s cut-back.
That missed opportunity was to prove costly for the hosts as Hearts went in front from a corner in the 55th minute. Kyle headed the ball into the path of Stevenson, who despite the close attentions of Ross Tokely managed to get in a volley that bounced over Esson and into the corner of the net.
Caley Thistle responded with a curling effort from Ross drifting narrowly wide of Kello’s upright, before Rooney had an effort deflected past the post. From the resultant corner, Palazuelos had to clear Tokely’s flick off the line.
Hearts then had a penalty claim when Elliot appeared to held inside the area by Innes, but referee Iain Brines waved away their claims.
After Rooney had passed up a decent chance to equalise when he blazed over, Hearts stretched their lead to two goals in the 69th minute.
Suso Santana’s trickery got him past Tokely and he picked out the unmarked Elliot who had little trouble in finishing from six yards to score his fourth goal of the season.
Inverness then made a double change with Stuart Golabek replacing the injured Innes, while Foran was introduced into the fray for Odhiambo.
Caley Thistle pushed hard to find a way back into the contest, but could not salvage anything from the game.