The home team trailed to an early Scott Brown goal before Zurawski drew them level just after the hour mark.
The stage was set for their new £3.5million signing Vennegoor of Hesselink, who had come on as substitute for Kenny Miller, and he did not disappoint. The Dutchman showed great alertness when Aiden McGeady's powerful shot came back off the post and he rammed the ball home from six yards to gain instant cult status amongst the home fans.
A Celtic victory had looked unlikely when Hibs made a marvellous start. Stephen McManus had already cleared off the line from the skilful Merouane Zemmama before Brown ran on to the Moroccan's shrewd pass to fire past David Marshall.
Celtic took time to re-group and Neil Lennon 's volley was eventually gathered by Zbigniew Malkowski. Shunsuke Nakamura then tested the Hibs' keeper with a well struck shot from fully 30 yards.
Nakamura was fouled on the edge of the box and there were strong appeals from the home crowd that Jay Shields' tackle was inside the box. Nakamura took the free-kick himself only to see it come back off the bar as Celtic started to recover from their early setback.
Just before half time Hibs took off the volatile Abdessalam Benjelloun, who had already been booked, but substitute Ivan Sproule should have done better than find the side netting after rounding Marshall.
Celtic upped the tempo at the start of the second half and Stephen Pearson burst through the middle only to knock the ball too far ahead, allowed Malkowski to clear.
A good run by new signing Lee Naylor ended with Zurawski gathering his cutback before cleverly side-stepping Jones and sliding his shot home.
The introduction of Vennegoor of Hesselink minutes before had galvanised the whole team, and after a weaving run by McGeady ended with a shot against the post, the new signing reacted fastest to force home the rebound.
Hibs tried desperately to get back into the match and substitute Chris Killen, who had come on for the tiring Zemmama, laid the ball off to Brown whose first-time effort went narrowly wide.
McManus found space in the box when his header from Nakamura's corner was just too high.
In a flowing move McGeady's pass found Vennegoor of Hesselink whose back heel reached Zurawski, but the Pole was denied a second goal when Shields blocked his shot at the expense of a corner.
Celtic were well in control by this stage and McGeady could have added to their lead but his strike ended up in the side netting.
The Celtic fans will be well pleased with their victory against the Hibs team who always give them problems. But the absence of Stilian Petrov from the 18 players who were stripped for action would suggest that the Bulgarian international has played his last game for the club.