Mikael Lustig notched his first goal for the Hoops in the 11th minute when he fired in from a Paddy McCourt corner but a disastrous mix-up between the Swedish defender and keeper Fraser Forster in the 53rd minute allowed Tim Clancy to equalise.
Lustig was involved again when Hibs skipper James McPake knocked the ball into his own net after Easter Road keeper Ben Williams had made a mess of a Filip Twardzik free-kick, but again poor defending by the champions allowed Paul Cairney to slip all too easily into their box and level with a drive.
The result may not have a significant impact on the SPL title race but it was a stark warning for Neil Lennon's men who learned on Friday that their first entry into the group stages of the Champions League in four years would see them take on Barcelona, Benfica and Spartak Moscow.
Scott Brown, Georgios Samaras, Charlie Mulgrew and Kris Commons dropped out for the home side, the latter to the bench, to be replaced by Tony Watt, Twardzik, McCourt and Lustig and it was the latter two, during a rather sedate start to the game, who combined for the opener.
When the Northern Irishman's corner from the right arrived at the feet of Lustig the Sweden defender volleyed it low past Williams from 10 yards. It looked at that point like it was going to be a stroll and Gary Hooper struck the woodwork for the Hoops twice before the break.
Forster's goal survived a scare when Griffiths' whipped-in free-kick from the right was met by Hibs' striker Eoin Doyle who struck the post with his close-range effort. The Parkhead defence failed to heed that warning. A long ball from Doyle initially offered little danger but Lustig and Forster hesitated allowing Clancy to nip the ball past both and knock into an empty net.
The home side restored their lead in the 67th minute when Williams spilled a good but not uncatchable Twardzik free-kick from 30 yards and as Lustig slid in to capitalise, McPake seemed to help the ball over the line.
However, that lead did not last long and in five minutes later slack defending again in the Hoops box allowed Cairney to ferret his way through before directing a low drive past Forster.
The Parkhead side drove forward in the final stages looking for the winner but found a Hibs side determined to hang on and take full advantage of their hosts' hospitality.