The victory lifted the reigning champions to two points behind Scottish Premiership leaders Hearts, with a game in hand.
Before kick-off, O'Neill revealed his caretaker spell in charge of the Glasgow giants was set to last a little longer, with the 73-year-old expected to be at the helm for Wednesday's visit of Dundee while Celtic complete the paperwork needed for the arrival of Wilfried Nancy as their new permanent boss.
Goals from Daizen Maeda and Arne Engels paved the way for Celtic's sixth win in seven matches under O'Neill, who enjoyed great success during his first spell as manager of the Hoops from 2000-2005.
A poor pass out from goalkeeper Raphael Sallinger enabled Reo Hatate to steal easy possession near the Hibs area. He squared for Maeda to roll the ball into an empty net in the 27th minute.
Less than a minute later, Celtic doubled their lead at Easter Road when Engels bravely headed in Hyun-Jun Yang's cross while taking a boot to the face.
Rangers held
Celtic almost put the result beyond doubt when Japan forward Maeda back-heeled the ball into the path of the on-rushing Marcelo Saracchi, but the full-back's shot struck a post.
Hibernian upped their game after half-time, with Martin Boyle's well-taken penalty, awarded for a Liam Scales handball, a deserved reward.
The hosts pressed hard for an equaliser, with Chris Cadden going close late on when his shot was saved by the legs of Kasper Schmeichel.
Hearts, the arch Edinburgh rivals of Hibernian, dropped points for the third league game in a row on Saturday with a goalless draw away to Motherwell.
Rangers saw their four-match winning league run under manager Danny Rohl, who replaced the sacked Russell Martin, end as Falkirk battled to a goalless draw at Ibrox.
The result left Rangers in fourth place - nine points adrift of Hearts.
Elsewhere, Nicky Devlin's goal 10 minutes from time secured Aberdeen's 1-0 win away to bottom-of-the-table Livingston.