John Souttar's last-gasp header stunned Celtic as Hearts secured a 2-1 victory on their return to the Scottish Premiership.
Hearts made the best possible start as Gary Mackay-Steven scored against his former club in the eighth minute to give the hosts an early lead. However, Celtic responded well to going a goal behind and they were eventually rewarded with an equaliser thanks to Anthony Ralston's superb solo effort (54).
Both sides pushed for a winner, but it was Hearts who struck late as Souttar capitalised on some poor Celtic defending to give his side the lead in the 89th minute.
Celtic still had time to fashion two chances to grab an equaliser but they found goalkeeper Craig Gordon in fine form as he denied James Forrest and Ryan Christie to secure all three points for his side and a winning return to the top fight.
For Celtic, it's the start new boss Postecoglou would have dreaded after their Champions League exit in midweek. It's a first opening-day defeat for Celtic since 1997, with Postecoglou still waiting for his first competitive win since taking over.
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How Hearts stunned Celtic...
Celtic have been accustomed to opening their season at home but they had to play a supporting role as Hearts raised the Championship flag. The visiting players had welcomed their opponents onto the park with a guard of honour and they were overly generous with their defending soon afterwards.
Carl Starfelt, a new arrival from Rubin Kazan failed to halt Josh Ginnelly's progress in an attempted tackle and then went to ground in a desperate attempt to stop Liam Boyce capitalising. The ball ultimately broke for Mackay-Steven to stroke home from six yards.
David Turnbull squandered Celtic's best first-half chances, twice failing to hit the target in space on the edge of the box and also hitting a free-kick into the wall.
There were other half-chances for the visitors. Craig Gordon comfortably saved Odsonne Edouard's header and long-range efforts from Callum McGregor and Ismaila Soro, while Liel Abada failed to test the goalkeeper after twice cutting inside.
But Hearts had opportunities to go into the break further ahead.
Liam Boyce headed not far over from a corner and the hosts were getting in behind the left side of Celtic's defence. Michael Smith fired into the stand when Boyce was well-placed in the middle before setting up fellow wing-back Alex Cochrane to volley wide.
Celtic levelled after some positive play from Ralston, whose only appearance last season came against Livingston in January when 14 of his team-mates were in self-isolation.
The defender got into the type of central attacking position Postecoglou demands of his full-backs, played a one-two with Edouard before swerving around an opponent and curling home with his left foot. It was the 22-year-old's first goal since December 2018 and the first goal Gordon had conceded in 12 club matches.
Hearts had been pinned back for much of the half but the introduction of midfielder Peter Haring turned the tide and Scott Bain had to scramble to stop Souttar's header.
Postecoglou responded by putting on Ryan Christie and debutant Kyogo Furuhashi, who had not even had time to train after his quarantine. The double switch almost paid immediate dividends with Gordon saving well from his Scotland team-mate.
- Hearts handed a debut to Beni Baningime after his arrival from Everton.
- Meanwhile, both Carl Starfelt and Nir Bitton came into the Celtic central defence and James Forrest made his first start of the season.
But Hearts were soon back on the front foot and Souttar headed past Bain with the goalkeeper stranded to spark wild celebrations at Tynecastle.
The drama was not over, though, and Gordon had to be at his best to deny his former side with two excellent stoppage-time saves from Forrest and Starfelt.
More disappointment for Postecoglou
Former Celtic midfielder Stiliyan Petrov, speaking on Sky Sports:
"It's a disappointing result but I do think we saw some positive play from Cletic, especially going forward.
"But unfortunately, when you talk about philosophy it is not just on the ball, it is off the ball as well.
"There are some worrying signs for Celtic, especially off the ball when the opposition believe and put pressure on Celtic.
"Then you can see there's a lot of work that needs to be done. But we have seen some positives. We can see what Ange Postecoglou is trying to implement but it will be a long, long road for him."
What the managers said…
Hearts boss Robbie Neilson: "I was delighted with them. Having 5,000 fans really helped us. Delighted to give the fans a good Saturday night.
"I thought Beni Baningime was sensational. He's only played three 45 minutes all through pre-season.
"John Souttar's a top player. Defensively and attacking, he's sensational. Delighted to get the goal, it's a massive three points but we've got to go and win at St Mirren next week."
Celtic boss Ange Postecoglou: "Hugely disappointing result. We got control of the game after a chaotic opening five minutes. We let ourselves down with some execution in the final third, and it was obviously disappointing to concede from a set play.
"I thought we were in control of the game when we scored but some of our shooting in and around the box let us down. Once we scored, I felt we had opportunities to win it.
"Not the way we wanted to start but we've got another game Thursday so no point just feeling sorry for ourselves - we had opportunities to win and we didn't do that.
"The board don't want me to fail, I think people are trying to make out there's some disconnect there. We all know what needs to be done and we're doing that collectively."
Man of the match - Beni Baningime
Stiliyan Petrov on Sky Sports: "He was really impressive today, especially in that kind of game because as a holding midfielder you have to really be composed.
"You have to work tirelessly because the team was always under pressure.
"He intercepted the ball very well and he's got great awareness. But every time he got the ball he managed to slow the play and he managed to control the game and give the team confidence.
"He was the outstanding player for Hearts because he was very relaxed, he knew his job and he did it perfectly."
Hearts now go to St Mirren on Saturday at 3pm in the Scottish Premiership, while Celtic go to FK Jablonec at 4.45pm on Thursday in their Europa League third qualifying round first leg.