Robbie Neilson’s side are the only senior side in Britain not to have tasted defeat this season and they had 7,000 fans cheering them on as James Keatings’ first-half goal proved decisive at Almondvale.
The home side were appealing for a penalty early on as Michael McKenna went down in the Hearts box under pressure, but the referee was not interested.
Adam Eckersey then found Keatings at the far post but he could not hit the target although he had a chance to atone from the penalty spot soon after when Jason Holt was fouled; his spot-kick was firmly struck but blocked by the legs of Livi keeper Darren Jamieson.
Sam Nicholson’s header was well saved before King deftly teed up Keatings (25) and it was third time lucky for the Hearts man who swept in his fourth goal in as many games from four yards.
Neil Alexander made an excellent save to deny Jordan White’s low shot from 12 yards while White was threatening again when he tested Alexander with a firm header.
It was the visitors who finished on top as Callum Paterson set up Nicholson, who shot straight at the keeper when he should have scored but it was not to matter as the victors’ thoughts turned to next week’s sold-out Edinburgh derby.