Former Arsenal and Liverpool midfielder Oxlade-Chamberlain joined the Glasgow giants after the conclusion of the transfer window earlier this month on a free transfer.
The 32-year-old had been without a club since leaving Besiktas in August but made himself an instant Celtic hero by curling in from the edge of the box.
Bottom-of-the-table Livingston looked set to earn an unlikely point after Robbie Muirhead's penalty had cancelled out a first-half opener from Marcelo Saracchi.
However, Oxlade-Chamberlain's late intervention means Martin O'Neill's men gained ground on Rangers in the latest twist in the title race.
Hearts' lead at the top of the table was only reduced to five points after Celtic loanee Stephen Welsh struck a late equaliser for 10-man Motherwell at Fir Park.
Nico Raskin gave the visitors an early lead and Rangers appeared set for victory when Lukas Fadinger was sent off for a lunge on Mikey Moore 12 minutes from time.
However, Welsh's equaliser gave Hearts further hope they can end the 41-year wait for a winner of the Scottish title other than the Old Firm duo.
Celtic are six points off the top but have a game in hand on the top two, who meet on Sunday when Hearts visit Ibrox.