Both sides struck twice inside the first 10 minutes at Almondvale as Benjamin Nygren and Yang Hyun-jun levelled for Celtic after Cristian Montano put bottom-of-the-table Livingston in front.
A fine strike by Nygren and Arne Engels' penalty before half-time eased the pressure on Wilfred Nancy with back-to-back wins since losing his first four games in charge of the Glasgow giants.
Celtic are now within striking distance of the Jambos and have a game in hand after Hearts lost for just the second time this season.
Derek McInnes' men never recovered from a nightmare start at Easter Road in a major blow to their quest to break a 40-year stranglehold of Scottish football by Celtic and Rangers.
"We didn't do the basics well enough, it's as simple as that," said McInnes.
"We've got to where we've got this season, not by being Barcelona but by doing the basics well and playing from that. We never did that well enough."
Jamie McGrath steered home Nicky Cadden's cross after just three minutes.
Victory hauls Hibs back into the running for the European places, but inflicting a serious blow to their cross-city rivals' title dream made the three points all the sweeter for David Gray's side.
Josh Campbell headed in a second just before half-time.
Kieron Bowie's strike three minutes into the second period then had some Hearts fans heading for the exit.
Yet, those who stayed nearly witnessed a memorable fightback.
Lawrence Shankland cut the arrears 15 minutes from time before Cammy Devlin set up a grandstand finish.
Hibs goalkeeper Raphael Sallinger needed to make impressive stops to deny Shankland and Beni Baningime as the home side clung on during six minutes of stoppage time.
Rangers remain six points behind Celtic after edging out Motherwell 1-0 at Ibrox thanks to Thelo Aasgaard's winner midway through the second half.