Goals from Ryan Christie and Oliver Burke secured a fifth straight Premiership win without conceding a goal since the winter break for the Scottish champions to maintain their six point lead at the top of the table.
The only negative aspect of the night for Celtic was the sight of Emilio Izaguirre being carried off on a stretcher in the closing stages, the Honduran left-back joining a lengthy injury list which is testing the strength in depth of Rodgers’ squad to the limit.
They still had more than enough to see off a Hibs side whose need for the certainty and fresh direction of a new manager is obvious.
Christie’s 10th goal of what is proving to be a hugely productive season for the attacking midfielder earned Celtic a half-time lead they certainly merited on the overall balance of play.
Yet Hibs could also take initially encouragement from an opening 45 minutes in which they showed plenty of ambition with a positive formation set out by caretaker boss Eddie May.
Ryan Gauld, operating just behind strikers Oli Shaw and Florian Kamberi, saw plenty of the ball. But despite some neat passages of play, the visitors were unable to trouble Scott Bain in the home goal.
Celtic, by contrast, carried a far more menacing edge to their work. Callum McGregor, remarkably making his 50th appearance of the season for club and country, was first to threaten for the champions when his shot was blocked by namesake Darren in the Hibs defence.
Scott Brown and Christie combined to forge a decent opening for Scott Sinclair but the winger’s shot was deflected narrowly wide of Ofir Marciano’s left hand post.
With Timothy Weah, Christie and Sinclair forming the advanced midfield trio behind central striker Burke, Celtic’s control of the contest steadily increased.
Christie was unfortunate to see a sweetly struck effort from 20 yards fly just wide, then Marciano was off his line sharply to block a close range shot from Weah who had been played in by McGregor’s fine through ball.
When Sinclair cut in from the left to curl a shot narrowly beyond Marciano’s left hand post, there was a growing sense that the breakthrough was coming. It duly arrived in the 24th minute.
Jeremy Toljan, making his first start for Celtic after an eye-catching debut as a substitute in Sunday’s win at St Johnstone, played a major role in the goal.
The on-loan Borussia Dortmund right-back advanced to play a neat one-two with Weah before cutting the ball back for Christie to steer a low right foot shot beyond Marciano’s left hand from around eight yards.
Hibs were presented with an opportunity to hit back almost immediately when McGregor was caught in possession by Kamberi who found Mark Milligan in space on the left of the penalty area.
But the Australian international lacked composure as he slashed his shot well wide of Bain’s right hand post.
Celtic skipper Brown appeared fortunate to escape a booking for a crunching foul on Vykintas Slivka in the 29th minute, a decision which Hibs found all the more contentious when referee Craig Thomson flourished his yellow card soon afterwards at Milligan for a similar challenge on Christie.
Dedryck Boyata, back at the heart of the Celtic defence after an injury absence, ensured his side went into the break ahead when he made a brilliantly timed penalty area interception to deny Shaw who had latched onto Sean Mackie’s fine through ball.
Hibs were forced into a change at the start of the second half, Mark McNulty replacing the injured Shaw. They found themselves under increasing pressure as Celtic resumed with intensity and purpose as they looked to make the game safe.
May made a second change, sending on Stevie Mallan for Gauld who had faded badly after his relatively promising start.
Celtic remained firmly on the front foot and Marciano made a stunning save to keep out Boyata’s thumping close range header from a Christie free-kick.
The relentless pursuit of a second goal by Rodgers’ men was finally rewarded in the 64th minute. Christie was the architect with a sumptuous through ball which set Burke free on the right hand side of the Hibs penalty area.
The on-loan West Brom man’s right foot shot took a deflection off Darren McGregor before looping over the helpless Marciano into the net.
McNulty had a chance to open his Hibs account and drag them back into contention when he burst through the middle of the Celtic defence but the on-loan Reading forward screwed his shot wastefully wide.
There was a sour note to the evening for Celtic when Izaguirre sustained his injury on the end of a foul from Darnell Johnson which might easily have earned the Hibs substitute more than the booking he received.
It was an incident which also denied Vakoun Bayo his debut for Celtic, the Ivory Coast striker having been ready to come on but then called back as Jonny Hayes instead replaced Izaguirre at left-back for the closing stages.
Celtic: Bain, Toljan, Boyata (Bitton 74), Simunovic, Izaguirre (Hayes 83); Brown, McGregor; Weah, Christie, Sinclair (Johnston 73); Burke. Subs not used: Gordon, Bayo, Lustig, Henderson.
Hibs: Marciano, Gray (Johnson 65), McGregor, Hanlon, Stevenson; Slivka, Milligan, Mackie; Gauld (Mallan 59); Shaw (McNulty 46), Kamberi. Subs not used: Dabrowski, Nelom, Omeonga, Bigirimana.