And this demolition also allowed Hearts to close the gap on title rivals Celtic to eight points after they were held 3-3 at home to Dundee United.
Skipper Paul Hartley was the architect of Hibs' downfall with a first half double to cap a superb performance. And top scorer Rudi Skacel was almost as influential as Hartley as he helped himself to his 16th goal of the season.
But Hearts had Scotland keeper Craig Gordon to thank for keeping out an early Hibs barrage. He made a fine save low to his right from Gary O'Connor's header and then denied Derek Riordan with a great save high to his left.
Thereafter Hearts were always going to run out winners as they grabbed the game by the scruff of the neck.
Hartley made a long bursting run to get on the end of Skacel's cutback and tucked away a neat low finish. Then Skacel pounced on a loose ball to smash a low 15-yard volley past Simon Brown.
And when Skacel was pulled down in the box by David Murphy, Hartley stepped up to hammer home the penalty and put Hearts out of reach.
Hibs' cause wasn't helped when Gary Smith stupidly elbowed Saulius Mikoliunas in an off-the-ball incident and the visitors were reduced to ten men.
Hearts capitalised on the extra player only five minutes after the break when Skacel left Steven Whittaker for dead and his cross was bundled home by young Callum Elliot.
There was no way back for Hibs and O'Connor's deflected 20-yarder was scant consolation for a bedraggled Easter Road outfit.