Two first-half goals from Rudi Skacel enabled Hearts to move into pole position in the SPL.
Skacel opened the scoring in the eighth minute with a wonderful left-footed strike from 20 yards.
The Czech midfielder made it 2-0 after 15 minutes, when he drilled home a Calum Elliot pass.
Allan Walker pulled a goal back for Livi after 62 minutes with a low drive from 22 yards out which gave Craig Gordon no chance.
Hearts had started slowly in their first two games under head coach Graham Rix, at Aberdeen and Motherwell but they were quick out of the traps in front of their own supporters.
There was no surprise when the home side took the lead in the eighth minute and even less surprise that the scorer was Skacel with his 12th goal of the season.
The Czech midfielder picked the ball up in midfield, sped towards goal shrugging off three Livi defenders before unleashing a drive from 20 yards out which gave Ludovic Roy no chance.
In the 15th minute, after a brief promise of a fight back by the Lions, the Tynecastle side found themselves two ahead and again Skacel was the scorer.
The impressive Roman Bednar chested the ball down to Elliot at the left hand side of the penalty area and when the youngster's cross came into the middle, the Czech star controlled the ball with one touch before slamming a left-footed drive past the helpless Roy.
The Livi keeper then made a good double save from midfielder Saulius Mikoliunas and then Bednar as the hapless visitors looked like collapsing.
Livi striker James McPake had a great chance from a Jason Dair corner just before the break but the youngster missed his header altogether from only eight yards out.
Normal service resumed as Hearts stormed into attack at the beginning of the second half.
Brilliant play on the right by Mikoliunas gave Bednar a golden opportunity from 16 yards out but the Czech striker's effort went wide, this time past the right hand post.
However, the visitors were back in the game just after the hour-mark.
When the ball broke from a Julien Brellier interception to midfielder Allan Walker 20 yards from goal, the Livi midfielder wasted no time in drilling a shot past Gordon and into the corner of the net.
Hearts, stung by the audacity of the Lions goal, stormed up the park and almost hit back immediately but Bednar's shot came back off the post.
A nervousness enveloped Tynecastle but in the 85th minute Hearts substitute Michal Pospisil, who had replaced Bednar minutes earlier, sent a high, swirling cross in from the right which fooled Roy but bounced off the far post.
Then, in a remarkable incident, Vincze sent a throw-in straight into the Hearts net but the 'goal' was disallowed.
Hearts: Gordon, Neilson, Pressley, Webster, Fyssas, Mikoliunas, Hartley, Brellier (Simmons 66), Skacel, Elliot (Cesnauskis 90), Bednar (Pospisil 77). Subs Not Used: MacDonald, McAllister, Berra, Wallace.
Goals: Skacel 8, 15.
Livingston: Roy, Mackay, Pinxten, Strong, Tierney, Brittain, Walker (Scott 84), Vincze, Dair, Dalglish (Snodgrass 82), McPake. Subs Not Used: McKenzie, Dorado, Boyd, Adam, Tesevic.
Booked: Tierney, Walker, Dalglish, McPake.
Goals: Walker 63.
Ref: A Freeland