Celtic turned in the "performance of their season" so far as they beat Hibernian to remain one point behind Scottish Premiership leaders Rangers, says Neil Lennon.
But they lost Albian Ajeti to injury, ruling him out of Thursday's Europa League trip to FK Sarajevo.
Hibs have not won at Celtic Park since January 2010, and goals from Callum McGregor, Ajeti and Mohamed Elyounoussi scuppered hopes of ending that record.
Celtic still have a game in hand.
The Easter Road side remain third, but they have played two games more than fourth-placed Aberdeen.
"It was 10 out of 10, the best of the season and one of the best of my time as manager, first or second time around," said manager Lennon.
"I thought we were outstanding and I thought the football we played was brilliant. I thought the control of the game was brilliant.
"We defended when we had to - really well - and it was just an outstanding all-round team performance. I'm pleased, it was a big game for us."
The Edinburgh side spurned plenty of chances. Christian Doidge, Kevin Nisbet and Joe Newell all fired over from close range.
Leigh Griffiths returned to the Celtic squad, the Scotland striker without a competitive game since a hat-trick against St Mirren in March. And he was joined on the bench by Odsonne Edouard, who was dropped in favour of summer signing Ajeti.
But the opening goal came from midfield, with McGregor finding a pocket of space outside the box and arrowing a low shot into the far corner past the outstretched hand of Ofir Marciano.
The goal did not rattle Hibs, though, and Doidge was close to drawing Hibs level when he sent Nisbet's cut-back over the bar from inside the box. Nisbet then shot high, with Martin Boyle also frustrated.
But they were punished for their missed chances as Celtic doubled their lead. Ryan Christie did well to hold on to the ball in the box under pressure, Jeremie Frimpong nudged his pass into the path of Elyounoussi, whose shot was saved, but Ajeti slotted home the rebound for his fifth goal this term.
That was to be the Swiss striker's last action, hobbling off afterwards, with Edouard back into the fray.
Celtic's two wing-backs were the cause of Celtic's threat, and Greg Taylor's cross found Frimpong on the run but the Dutchman side-footed over. Scott Brown forced a good save from Marciano and seconds later the Israeli goalkeeper had to tip over from David Turnbull, who replaced Christie at the break, as Celtic looked for a third goal early in the second half.
Newell could not find the target for Hibs from inside the box, and Doidge had a shot charged down, but by this time the chances from the visitors were at a premium as Celtic dominated possession.
And Elyounoussi killed the game with a third goal when he strolled on to Turnbull's through ball to slip the ball under Marciano.
Man of the match - Jeremie Frimpong
What did we learn?
Celtic were criticised in midweek despite beating FC Riga to reach the play-off round of the Europa League.
Over the 90 minutes against Hibs they did wobble at times despite their early lead, but improved as the game went on with Taylor and Frimpong at the heart of sparking Celtic into life when they needed it.
Turnbull is also beginning to settle into life at Celtic after his move from Motherwell, and he impressed after replacing Christie at half-time.
Hibs had plenty of moments in the Celtic box and as always looked a threat on the counter attack, but they were not clinical enough.
What they said
Celtic manager Neil Lennon: "We were up against a good side who had won all their away games.
"It was a good test for us, and I thought we came through it with flying colours. It was a brilliant team performance, absolutely brilliant."
Hibernian manager Jack Ross: "I've no complaints over the end result, but first half I thought we were very good, there were aspects of our performance that were very good. We found ourselves in good areas of the pitch regularly, but were not clinical enough.
"It's unusual for us because we're normally very good at that. We just fell a little bit short today but our working to get ourselves into that area of the pitch was good."
Celtic will aim for a place in the Europa League group stage when they travel to FK Sarajevo on Thursday. They return to domestic action next Sunday away to St Johnstone.
Hibernian host Hamilton on Friday evening, their last engagement before the international break.