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 appeared to knock 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 yesterday 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.
To add further to the feelgood factor in the east end of Glasgow before the game, Celtic paraded two of their three new signings.
Nigeria central defender Efe Ambrose, who signed a three-year contract after an undisclosed fee was agreed with Israeli club Ashdod and 27-year-old Venezuelan striker Nicolas Fedor - nicknamed Miku - who arrived on a year-long loan from Spanish side Getafe, were given a warm welcome from the fans.
Absent was the third recruit, 25-year-old Slovakia goalkeeper Lubos Kamenar from French side Nantes.
Scott Brown, Georgios Samaras, Charlie Mulgrew and Kris Commons dropped out, 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 with little hindrance from the static home defence.
It looked at that point like it was going to be a stroll in the sunshine for Lennon's men, more so when Gary Hooper crashed a shot off the crossbar in the 20th minute from 14 yards after being set up by James Forrest.
As the Hoops dominated against a helpless looking Leith side, Williams was forced into a good save from Victor Wanyama's drive before Watt, who scored a brace in his first start for Celtic in last week's 4-2 win at Inverness, sent his angled drive over the bar.
Forrest and right-back Adam Matthews both came close with efforts as the procession towards the Hibees goal continued.
In the 38th minute, moments after Hibs striker Leigh Griffiths' spectacular overhead kick from six yards following a rare foray in to the Celtic box had cleared the bar, Watt missed a golden chance to score his first competitive goal in front of the home support.
The 18-year-old striker was sent clear of the square Easter Road side's defence by Wanyama but although the former Airdrie United player was calm enough to flick the ball over the onrushing Williams, he missed the target.
Hooper then struck woodwork for the second time when he headed a Matthews cross off the near post.
Jackson Irvine came on to make his competitive debut at the start of the second half, replacing Wanyama but within moments 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 goal stung Celtic back into action and McCourt ended a trademark mazy run by sending his shot from 14 yards just past the post.
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.
Commons replaced McCourt and when the Scotland midfielder sent in a free-kick from the left, it was cleared only to Twardzik who skied the ball over the bar.
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.