Just hours before kick-off, Celtic announced that Frenchman Wilfried Nancy will take over at Parkhead from Thursday after a successful spell at MLS side Columbus Crew.
O'Neill was given a hero's reception at full-time after masterminding seven wins in eight games since returning to the club he first managed between 2000 and 2005.
Daizen Maeda scored the only goal as Celtic failed to hit top gear but ended the night in a stronger position as their title rivals stumbled once more.
"To get a reception like that was pretty special" said O'Neill, 73.
"The bottom line is not only have the players done it, they've made me feel very young, which I'm not. Restoration of confidence was most important and they really stepped up.
"I'm relieved to win. I thought we could have put the game to bed earlier and it got a bit nervy at the end, but we've won, which keeps the club going."
Nancy's first match in charge will be a top-of-the-table clash against Hearts on Sunday.
But after a blistering start to the campaign raised hopes of ending the Old Firm's 40-year stranglehold on Scottish football, the Jambos have won just once in their last six games.
Bruce Anderson's 90th-minute equaliser salvaged a 1-1 draw for Kilmarnock at Tynecastle.
Hearts now lead Celtic only on goal difference, having played a game more than the defending champions.
Rangers are nine points behind the top two after needing a 98th-minute penalty to salvage a 2-2 draw at Dundee United.
Zac Sapsford and Amar Fatah twice put United in front at Tannadice.
Jayden Meghoma's long-range strike levelled before half-time but Rangers were headed for a first league defeat on the road for nearly a year until Nedim Bajrami converted a controversial stoppage-time penalty.