Hibs made it six consecutive away victories with two goals in the final seven minutes to deny brave Livingston.
Defender Greg Strong blazed in a shot from 12 yards late in the first-half to reward Livingston's good display.
Hibs poured forward after the interval and looked to be out of luck until Dean Shiels slotted home after good work from fellow substitute Ivan Sproule.
Garry O'Connor completed the comeback when his deflected strike looped over goalkeeper Roddy Mckenzie.
Hibs kicked off with the backing of almost two-thirds of Almondvale Stadium behind them but did not start well.
Tony Mowbray's side were clumsy in possession and failed to find any passing rhythm against spirited opponents.
And Livi were first to threaten with Robert Snodgrass - who had netted three times in his last two games - firing a speculative shot wide.
Visiting goalkeeper Zbigniew Malkowski was caught out when he came to collect Jason Dair's lofted free-kick but lost out to Neil Barrett, whose header dropped wide of the target.
The impressive Barrett then beat Kevin Thomson in the tackle, but could only drag an 18-yard effort wide of Malkowski's post.
Thomson responded with a 20-yarder which McKenzie could only palm away and O'Connor could not connect fully with the follow-up, allowing the keeper to gather on his line.
Barrett nodded a Paul Tierney free-kick just over and James McPake headed wide as the home team pressed.
Thomson's dipping volley drifted over five minutes before the break, before Livi took a lead their play deserved in the 42nd minute.
Barrett's free-kick caused havoc in the box and McPake was able to lay the ball off to Strong, who swept home a fierce shot.
Derek Riordan should have levelled on the stroke of half-time, but hesitated to allow McKenzie to gather as he raced in on goal. The Hibs striker missed another great chance early in the second half when he sliced wide of the target from eight yards.
O'Connor had a downward header flicked away by McKenzie but the visitors had a lucky escape when Strong almost snatched an unlikely second with an awkward over-head kick.
Malkowski then had to get down smartly to push away a 20 yard strike from Richard Brittain. O'Connor tried his luck with a long range lob but McKenzie, who had been at the edge of his area, raced back to tip the ball over.
Riordan almost deflected in a shot from Shiels but again the ball flew wide.
Livingston appeared to be holding on for their first win of the season but Hibs' luck turned when a shot from Sproule was deflected into the path of Shiels and he slipped the ball in from seven yards.
A few minutes later Hibs were in front when O'Connor's 25-yard strike looped up from a deflection off Allan Walker and left McKenzie helpless as it hit the back of the net.
Livingston: McKenzie, Mackay, Pinxten, Strong, Tierney, Brittain, Neil Barrett, Walker, Dair (Dorado 88), Snodgrass (Scott 60), McPake (Dalglish 60). Subs Not Used: Roy, Pereira, Miller, Adam.
Booked: Dalglish, Tierney, Walker. Goal: Strong 42.
Hibernian: Malkowski, Caldwell, Hogg, Rudge, Murphy, Scott Brown, Beuzelin (Shiels 58), Stewart, Thomson (Sproule 58), O'Connor, Riordan (Fletcher 78). Subs Not Used: Simon Brown, Glass, Morrow, Smith.
Goals: Shiels 83, O'Connor 86.
Ref: D McDonald