Goals from David Murphy, Dean Shiels and Garry O'Connor gave Hibernian their first win of the season.
Murphy opened the scoring after 40 minutes, when he cut in from the left before sending a curling shot into the top corner of the net.
Dean Shiels doubled the lead almost immediately when he evaded a clutch of Livi defenders before slotting home.
Garry O'Connor lashed home the third on 53 minutes after Gabor Vincze lost the ball in his own half.
Hibs almost drew first blood after 10 minutes, when Michael Stewart's mis-directed cross sailed towards goal and just sneaked over the crossbar.
Dean Shiels then did well to fight off three opponents, before trying to set up David Murphy, but his cross was diverted for a corner.
That gave Derek Riordan the opportunity to pinpoint Guillaume Beuzelin in front of goal, but he nodded just wide of the target from about a yard out.
At the other end of the park, James McPake's flick was met by Martin Scott, but his angled drive curled away from goal at the last minute.
Hibs were unlucky not to break the deadlock midway through the first half, when Michael Stewart fed the ball out to Riordan on the right flank and he squared into the box, presenting O'Connor with a shot from a few yards out.
However, a block from David McKay was enough to send the effort over.
The breakthrough finally came after 40 minutes when Hibs took the lead after a superb individual goal from Murphy, which saw the left-back take the ball to the edge of the area before sending his shot into the top corner of the net.
Hibs were celebrating again within a minute, when Shiels exchanged a one-two with Brown, before rounding the Livingston goalkeeper and slotting home.
Livingston were given little respite after the interval and soon O'Connor was tearing into the box, with Riordan trying to keep up on his left.
With Livi goalkeeper McKenzie bearing down on O'Connor, he tried to set up Riordan for the shot but the youngster failed to meet the pass and the opportunity was lost.
Seconds later, Stewart robbed Vincze of possession before threading the ball through to the burly striker and, this time, O'Connor sent the ball low and hard past McKenzie.
Riordan became the provider shortly after, but substitute Steven Whittaker's shot was held by the goalkeeper.
With 10 minutes remaining, there was an air of resignation about Allan Walker's feeble attempt at pulling a goal back and the effort sailed harmlessly over the crossbar.
Emmanuel Dorado's deflected drive a few seconds later was little better and Hibs goalkeeper Zbigniew Malkowski was barely troubled.
Most of the fight had gone out of Livingston by the time the final whistle sounded and looked like a team willing to settle for the defeat long before then.
Hibernian: Malkowski, Whittaker, Hogg, Smith, Murphy, Scott Brown, Beuzelin, Stewart, Shiels (Thomson 66), O'Connor (Morrow 57), Riordan (Fletcher 86). Subs Not Used: Simon Brown, Glass, Konte, Murray.
Goals: Murphy 40, Shiels 42, O'Connor 53.
Livingston: McKenzie, Mackay, Dorado, Brittain, Tierney, Adams, Vincze (McLaughlin 76), Walker, Tesevic (Dorrans 51), McPake (Snodgrass 37), Scott. Subs Not Used: Roy, Adam, Miller, Pereira.
Booked: Walker, Dorado, Vincze, Scott, Tierney, Mackay.
Ref: K Turner