Ki Sung-yueng doubled the visitors' lead with a fine low drive just after the hour mark to seal the points.
Hoops boss Neil Lennon was surprised with the quality of his team’s performance.
"I thought we were outstanding in the second half.
"It was probably more than I could have expected at this stage of the season.
"So I am obviously delighted with the performance, result and clean sheet.
"I thought the players adapted brilliantly.
"We got a break with the goalkeeping mistake but we had good control of the game and going forward we were excellent."
Hibernian boss Colin Calderwood denied the apparent uncertainty surrounding his future had had an effect on his side.
Asked if he was confident speculation had not played a part in the defeat, he said: "Absolutely. 100%.
"We just don't have the experience to get through 90 minutes at the moment.
"We won't play Celtic every week.