Manager Brendan Rodgers hailed his "excellent" Celtic side as they met his demand of "building on our recent success" by fighting back from a goal down to stretch Hibernian's winless run at Parkhead to 22 games.
Travelling to the Scottish Premiership champions amid a stunning run of form that included victory over Celtic at Easter Road in February, third-place Hibs opened the scoring when Martin Boyle capitalised on Auston Trusty's poor defending.
The Australia forward had already passed up a glorious chance, but Celtic always looked dangerous in attack and levelled when Nicolas Kuhn got on to a ball in behind before rounding goalkeeper Jordan Smith and finishing.
Four minutes later, German winger Kuhn turned provider with a delightful dink beyond the Hibs defence for striker Adam Idah to power Rodgers' side ahead at the break.
And despite a bright start to the second period, with Rocky Bushiri heading narrowly wide from a long throw, the game was put beyond Hibs when Reo Hatate stroked in a third just before the hour.
"The performance level overall was excellent," Celtic boss Rodgers told BBC Scotland. "We went one behind, but we were doing so many good things in the game.
"My big message was about building on our recent success - that's what the club is all about. We want to go into [the Scottish Cup final] in a really good way, for that we need to work."
The defeat is just a second loss in 20 league games for David Gray's Hibs, who still hold a three-point advantage in third but have played a game more than Aberdeen, who could close that gap with a win at Rangers on Sunday.