Celtic now four points clear of Rangers
Goals in each half from skipper Stephen McManus and top scorer Scott McDonald were enough to give Gordon Strachan's men the points and keep the pressure on Rangers who have two games in hand on their Old Firm rivals.
Celtic boss Strachan was pleased his side got the result they merited after creating a host of chances.
"It was a terrific game, and it shows that at this time of year you can still play good football," he said.
"Hibs were after the points they needed to get to third, we were after the points to keep the league going, and so it made for a smashing game.
"I thought we deserved it because we created more chances."
"Sometimes you're unlucky, as we proved this year that you can make a lot of chances and not be that lucky.
"Paul Hartley and Gary Caldwell were the best men on the pitch."