When Kris Commons scored the opener in the eighth minute a heavy defeat looked inevitable for Hibs, who have now lost three in a row.
However, the Easter Road club fought back well and only a string of magnificent saves from Forster to deny Abdellah Zoubir and Sam Stanton kept Celtic in front before late goals from Virgil van Dijk, Teemu Pukki and Commons again, sealed the win.
The English goalkeeper has now gone over 14 hours without conceding a goal and is close to emulating Charlie Shaw's club record run of 10 consecutive clean sheets from the 1920s.
The Hoops have now won 11 matches in a row and while most of the attention has been on the forwards, manager Neil Lennon singled out Forster as the standout in his team.
"I thought some of his saves were awesome, I have to say. He is one of the only types of goalkeepers who can make those saves," said Lennon.
"For someone who is so big -- and he has a great presence in the goal -- his agility is fantastic. I think he's got a huge career ahead of him and he's made giant strides here.
"It's a nice treat to have. Sometimes when we are on top he's not had much to do but he's really earned his corn today."
Commons scored a double for the third match in a row as he fired Celtic into a fourth-minute lead before expertly despatching a 90th minute penalty after Pukki had been bundled over by Alan Maybury.
The in-form midfielder has now bagged 21 goals for the season but he was quick to highlight the contribution of Forster to his side's run of good form that sees Celtic sit 15 points clear of Aberdeen at the top of the Scottish Premiership as they extended their unbeaten start to the season to 22 games.
"Each week it's going to get harder and harder but the boys at the back and big Fraser Forster deserve massive credit for today," Commons said.
"There were some world class saves that keeps the clean sheet run going but also our winning streak."
Van Dijk's magnificent free-kick was the pick of the goals at Easter Road as the defender curled his set piece into the top corner from 22 yards.
The Dutchman's contribution also drew tributes from his manager.
"He's been threatening to do that for a while and I wasn't happy with the way the free-kicks had gone before that," Lennon said.
"Our two previous free-kick were lacking in imagination. I thought they were a wee bit hopeful rather than being hit with conviction but he's gone up there and he's unstoppable. I think if you had two goalkeepers in there they wouldn't have stopped it.
"I think he has been so consistent and he's a class act. He's like a Rolls Royce when's he playing.
"He's technically so gifted and physically he's a great specimen and he's certainly had a great season so far."
Celtic have yet to taste defeat in the defence of their title and have dropped just six points all season and Lennon is keen for the run to continue.
"I think we have to go after the records as we might not get in this position again. We have to maximise it and it gives the season just that little extra incentive," the Celtic manager said.
"People think that the league's gone now but we have our own targets to try and achieve. You can see that in the focus that the players have."
Source : AFP