Swedish international striker Henrik Larsson produced a first-half double as Celtic secured their ninth win in a row to leapfrog Hibernian into top spot in the Premier League.
Substitute Mark Burchill added a third for the rampant Parkhead side which ended Hibernian's unbeaten start to the season.
The Celtic Park showdown never needed any pre-match hype as the visitors went into the game on the summit and facing their biggest test so far.
Nevertheless Celtic, who started a day a point behind their opponents in second place but with 100% record, were in awesome mood and showed that the impressive beginning under new boss Martin O'Neill is no flash in the pan.
The former Leicester City manager has given the Glasgow side some resilience but against Hibernian they served up a tasty dish of attacking flair and it was once again Larsson who led the way to bag his seventh and eighth goals of the season.
The pressure on the Hibernian defence was relentless from the first whistle as the home side made a whirlwind start.
As early as the fourth minute Hibernian survived a penalty scare when Paul Lambert went down under the challenge of Paul Fenwick, but referee John Rowbotham waved away the protests.
Jackie McNamara then conjured up the first clear cut chance when he cut into the box from the right wing before unleashing a powerful left-footed shot just past the post.
The home side's tails were clearly up and Lubo Moravcik tried his luck from over 20 yards out in the 13th minute with a dipping drive which Nick Colgan did well to push over.
Celtic's confidence was replaced by concern in the 14th minute when Alan Stubbs collided with team-mate Lambert and the defender was stretchered off.
But those feelings of worry were soon forgotten in the 19th minute when the home side took the lead.
Colgan came rushing out to clatter into Alan Thompson on the very edge of the box before Larsson coolly stepped up to send the Hibernian goalkeeper the wrong way from the spot.
The visitors did make a rare break into the Celtic half in the 23rd minute and it almost brought them the leveller when John O'Neill ran through unchallenged before hitting a right footed drive that keeper Jonathan Gould brilliantly saved to his left.
Celtic, however, pressed for a second and in the closing stages of the half it seemed they were camped out in the Hibernian box as they looked to wear down their opponents.
Striker Chris Sutton should have bagged his seventh goal of his Celtic career in the last minute of the half when he peeled away from the defence but he glanced his header, from Thompson's free kick, past the post.
Moments later and Moravcik should have doubled their advantage when Thompson again played him through on goal, but he blazed his effort straight at a relieved Colgan.
But there was still time for Celtic to bag their second of the afternoon and they did it at just the right time.
Lambert brilliantly played the ball out to Moravcik unmarked on the left flank and he delivered an inch perfect cross for Larsson to head home.
The home side began where they left off after the restart and Thompson went agonisingly close a minute into the second period when he rifled a shot just inches wide from 20 yards.
The former Aston Villa man was looking for his second goal in as many games and in the 58th minute he hit a rasping 25-yard free kick which flashed just past the post.
Four minutes later Colgan had to be brave to keep his side's faint hopes alive when Larsson played Stilian Petrov through but the Bulgarian international's first touch took it away from him and the keeper saved low at his feet.
Larsson himself had the scent of a hat-trick and only another great stop from Colgan denied the Swede a treble after hitting a first effort from just inside the box.
However, Hibernian were refusing to fold and in the 79th minute they gave the home side a warning that they could not afford to be complacent when Gould brilliantly saved Stuart Lovell's effort from close range.
This sparked O'Neill's men back into life and in the 81st minute Sutton and McNamara should have secured the points when the £6million man rounded Colgan on the ground but Franck Sauzee cleared off the line and the Scotland international followed up to fire well over.
Nevertheless there was still a time for Celtic to grab their third of the match in the closing seconds as Sutton beat the offside trap and unselfishly squared the ball to substitute Burchill who side footed into the empty net.