The hosts looked to be on course for a narrow victory over the division’s basement side as they led 1-0 for much of the game following a 31st-minute strike from Jason Cummings.
However, Ibra Sekajja levelled for the visitors in the 88th minute only for Franck Dja Djedje to snatch the winner for Hibs just a minute later.
The win also stretches Hibernian’s unbeaten record to 14 games and takes them five points clear of third-placed Rangers in the table.
Hibs started strongly against a Livingston side who had lost their last four matches with Cummings seeing a shot blocked before he tested Livi ’keeper Darren Jamieson from 20 yards.
Jamieson also kept out a half-volley from Martin Boyle, who then hit the bar with a header from an acute angle.
Cummings wasted a good chance when he shot wide after being put clean through but he made amends shortly afterwards with a composed finish after being played in by Liam Craig.
Jamieson denied Boyle once again and Cummings had a shot cleared off the line but Livingston held firm until the break.
Hibs continued to dominate after the restart with Craig, Boyle and Cummings probing away at the Livi defence, the latter going closest to a second goal when he fired over.
Jamieson saved a free-kick from Craig with 13 minutes remaining and also denied Djedje, but Livingston stunned the home crowd when Sekajja tapped home to level in the closing stages.
However, Djedje had the final word as he rose highest to head home Lewis Stevenson’s cross via the post.