Hibs snatched their sixth successive away win with two goals in the last 10 minutes from Dean Shiels and Garry O'Connor.
Until then, Livingston looked to be on the verge of an upset after leading through a first half goal from Greg Strong.
Hibs threatened first when David Murphy took a pass from Kevin Thomson and skipped past James McPake, but sliced his left-foot shot narrowly wide.
But Livingston hit back immediately and Neil Barrett's header drifted just a foot wide with Zibi Malkowski exposed.
Roddy McKenzie came to the home side's rescue midway through the first half when he leapt to his right to beat out a Thomson shot and the goalkeeper was alert enough to smother O'Connor's follow-up effort.
Livingston impressed as they threatened an uncertain Hibs' defence on several occasions in the first half, and McPake should have hit the target with a header from a Paul Tierney cross.
Hibs did not heed the warning and fell behind three minutes from the break. McPake laid the ball into the path of Strong, who drilled a 12-yard shot high into the net with the Hibs defence in disarray.
Derek Riordan had a chance to equalise on the stroke of half-time when Scott Brown played him in, but McKenzie managed to force him wide and the chance was lost.
The striker had another great chance 10 minutes into the second half when Guillaume Beuzelin set him up, but he blazed his shot over the top.
McKenzie then clawed away an O'Connor lob from under his crossbar as Hibs came close again.
The goal finally came eight minutes from time when an Ivan Sproule shot broke to Shiels at the back post and he tucked the ball into the corner of the net. O'Connor then snatched the winner with a 25-yard shot which deflected off Allan Walker to loop over McKenzie.