A brilliant double from Rudi Skacel fired Hearts back to the top of the league and gave head coach Graham Rix his first Hearts win.
Hearts came out the blocks strongly and were two goals up inside 15 minutes both from the lethal left foot of Skacel.
Young striker Calum Elliot had wasted a couple of early half chances, but Skacel settled the nerves with a brilliant opener that must be a candidate for goal of the season. He left three Livingstone defenders trailing in his wake before looking up and firing a vicious 20-yarder into the top corner of Ludovic Roy's net.
Livi had barely had the chance to regroup when Skacel had added to his account. He took a clever cross from Calum Elliot and hit a low left-foot shot into the bottom corner from 12 yards.
It looked at this point as though Livingstone were in for a real hammering, but Hearts got sloppy in front of goal and lost their grip on the game.
Comeback man Roman Bednar hit the post from a tight angle and Skacel was only inches away with a 25-yard free-kick.
But Livi grabbed a lifeline after 63 minutes with a spectacular long-range goal from Alan Walker. It was more than they deserved at that point, but they got a lift and began to compete much more in the game.
Having said that, Hearts hit the post again with a speculative effort from Michal Pospisil and then Paul Hartley missed a glorious opportunity from only 10 yards from Pospisil's cut-back.
The match ended in controversy when Livingstone had the ball in the net only minutes from the end from Gabor Vincze's long throw-in. Livingstone claimed the ball had been deflected on its way in, but referee Alan Freeland saw nothing wrong and awarded Hearts a goal kick.
It would have been a travesty had Hearts not held out because they could easily have won by three or four goals given their domination of the game.