That was not the only surprise of the day in the division, with Stranraer securing only their sixth win of the campaign with a 1-0 victory away to Queen's Park to climb off the bottom.
Elsewhere, Alloa Athletic secured a thrilling 4-2 win over Stenhousemuir, who drop to the foot of the table.
That means only three points separate the bottom four now.
Liam Buchanan gave Livingston an early lead at Bayview, but substitute Jamie Insall equalised with a quarter of an hour remaining.
Scott Robinson grabbed the winner three minutes later.
At Hampden, Willie Gibson scored the only goal of the game for Stranraer, who now rise to eighth, with a 20-yard effort on the hour mark to defeat the Spiders.
Alan Cook put Stenhousemuir ahead after nine minutes against Alloa, but Kevin Cawley, Greig Spence and Jordan Kirkpatrick turned the contest on its head before half-time.
Kirkpatrick completed his brace after the interval, with Oli Shaw netting a late consolation for the home side.
East Fife stunned runaway leaders Livingston with a 2-1 victory in Scottish League One.