The ex-Derby County striker was on hand on eight minutes to take advantage of a defensive mix-up, seeing both centre halves try to head the same loose ball away and, as the ball broke into his path, the English forward calmly slotted the ball past Ben Williams.
Hibs tried to find an immediate response and may consider themselves unlucky not have earned a penalty when James Collins' run into the area was brought to an abrupt end by a challenge from Efe Ambrose, but referee Craig Thomson decided against awarding the spot kick.
Celtic's defending in the first half was nervy at times and when a Hibernian corner broke off the head of Virgil van Dijk, the Hoops were grateful that Fraser Forster was alert enough to claim the ball before any the home side's attackers.
Forster needed to be watchful again, just before the interval, when Samuel Stanton worked a shooting chance and his effort drifted narrowly over the bar.
Terry Butcher's side, who lost 3-2 at home to St Mirren last weekend, continued to enjoy a bright spell early in the second half and went close to an equaliser when first Abdellah Zoubir and then Stanton produced fine saves out of Forster.
With less than a quarter of an hour to go, the Hoops found a second goal when Van Dijk's well taken free kick from 25 yards out was too good for Williams in the Hibs goal.
On 82 minutes, Celtic sealed the points when Teemu Pukki shot from the corner of the box was only parried by Williams into the corner of the net.
In the last minute of the 90, Hibs defender Alan Maybury seemed to lose his head with what looked a needless challenge on Teemu Pukki as the Finnish striker was running away from goal to give the visitors a penalty.
Kris Commons scored his second from the spot to give Celtic a 4-0 victory their performance and even Hibernian's, arguably didn't merit.