Thoughts that it could take a few weeks for Burley's League of Nations side to click were quickly dispelled in a dominant display.
The former Derby and Ipswich boss gave debuts to recent signings Bednar, Skacel and Edgar Jankauskas and all three showed that they are capable of standing up to the physical challenges of the SPL - and that they know their way to goal.
Kilmarnock took the lead after a cagey opening when Stevie Naismith, by far the home side's best performer, latched on to Peter Leven's long throw in the 12th minute to coolly dispatch the ball under Craig Gordon from a tight angle.
Any thoughts that this might be Killie's day were killed when Hearts equalised within a minute after the three new boys combined for the goal.
Jankauskas' cross from the left was met cleanly by Bednar, but Killie keeper Alan Combe blocked his effort. The ball rebounded to the unmarked Skacel, who slammed it high into the empty net.
Killie held out until half-time, but were behind a minute into the second half, with the three new boys all involved again. Skacel's cross was met by Jankauskas, who nodded the ball back to Bednar whose header crept over the line via the upright.
Hearts added a third when Saulius Mikoliunas rifled a beautiful 25-yarder into the far corner in the 61st minute.
Kilmarnock fought their way back into the match thanks to Gordon Greer's 74th minute header from a Gary Locke free-kick.
However, hopes of a home comeback were short lived as Locke upended Jankauskas in the penalty area a minute from time and Paul Hartley stepped up to smash the ball into the corner.