The rock-bottom visitors looked set to earn an unlikely point on Wednesday night after Robbie Muirhead's penalty had cancelled out a first-half opener from Marcelo Saracchi.
But with the clock into the second minute of time added on, second-half substitute Oxlade-Chamberlain curled an effort into the far corner to give his team the win that moves them to within six points of leaders Hearts (57), with a game in hand.
Former England international Oxlade-Chamberlain, now 32, previously played in the Premier League for Southampton, Arsenal and Liverpool before two seasons in Turkey with Besiktas.
"He's been a class player, there's no question about it," Celtic manager Martin O'Neill said.
"He's played for big teams and performed brilliantly so I'm just really delighted to have him and getting him onto the field as well too.
"It was a great strike and I was right behind it when I saw it. The minute it left his foot, I thought, 'this is in'."
Glasgow rivals Rangers' title hopes suffered a damaging blow as Stephen Welsh's late leveller gave 10-man Motherwell a deserved 1-1 draw at Fir Park.
Midfielder Nico Raskin gave the visitors, who had former Western Sydney Wanderers midfielder Oscar Priestman enter the contest at halftime, the lead with a well-worked goal after six minutes.
Lukas Fadinger was sent off for a 78th-minute foul, but 11 minutes later Welsh drove in a dramatic leveller to leave Rangers five points behind Hearts.
Elsewhere, Kilmarnock clawed themselves closer to safety thanks to a Tyreece John-Jules hat-trick in an enthralling 4-3 victory over St Mirren.
Aston Villa loanee Ben Broggio marked his full league debut with what proved to be Falkirk's winning goal after Dundee's Yan Dhanda missed an added-time penalty in their 1-0 defeat.
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