Nicolas Kuhn opened the scoring inside three minutes before Callum McGregor's strike doubled the visitors' advantage before the 20-minute mark.
Victory takes the Scottish champions two points clear of Rangers and Dundee, who were both victorious on Saturday, at the top of the table.
Despite Rodgers' frustration at a lack of signings to strengthen his squad with one eye on a return to the Champions League next month, Celtic have started the season in fine form.
They hit four goals past both Manchester City and Chelsea in pre-season and dished out a 4-0 hammering on Kilmarnock to begin their title defence last weekend.
By contrast, Hibs have endured a tough start to David Gray's time in charge.
They were beaten 3-0 at St. Mirren to open their league campaign and never recovered from conceding from Celtic's first attack.
Josef Bursik saved Kyogo Furuhashi's shot, but James Forrest pounced on the rebound to square for Kuhn to tap into an empty net.
Celtic should have doubled their lead when Furuhashi latched onto a wayward back pass and fired wide.
But just seconds later McGregor took aim from outside the box and found the top corner.
The Celtic captain this week announced his retirement from international football and the onlooking Scotland boss Steve Clarke was shown the quality he will now miss.
Bursik denied Furuhashi again with a fine save and McGregor had a deflected effort come back off the post as Celtic passed up a series of chances to add to their lead after the break.
Hibs rarely threatened but were close to setting up a nervy finale when debutant Kieron Bowie smashed off the crossbar from a narrow angle.
The sides will meet again next weekend in the League Cup but on this evidence, Hibs will make the trip to Glasgow with trepidation rather than expectation.
