Two goals from teenage striker Scott Brown gave Hibs their fourth successive win.
The youngster struck in each half - his first goals for the club - to give Hibs victory.
It was another encouraging performance from the Edinburgh side who included four Under-21 players in their ranks.
Fernando Pasquinelli had an early chance for Livingston when he turned Paul Fenwick on the edge of the box but his finish was lazy and Daniel Andersson saved comfortably.
Hibs hit back and Alan Main did well to block a 25-yard shot from Grant Brebner before the goalkeeper produced an excellent save to palm a Derek Riordan shot to safety.
There were chances at both ends and another great run from Pasquinelli should have produced more but his low cross evaded Barry Wilson.
Hibs took the lead ten minutes before the break when a slip by David McNamee gave Scott Brown the opening and he placed the ball carefully beyond Main.
Livingston almost equalised three minutes into the second half when a wayward clearance from Darren Thompson fell to Pasquinelli and his effort was brilliantly saved by Andersson.
But Brown volleyed in his second goal in the 68th minute after Steven Whittaker had headed a Jarkko Wiss free-kick back across goal.
Livingston tried to get back but Andersson produced another wonderful one-handed save to deny David Bingham, playing his last home game for the club.
There was some late consolation for Livingston when Pasquinelli drilled a low shot through the legs of Andersson to score.