A goal from substitute Eamonn Brophy 17 minutes from the end earned Hamilton a precious point against 10-man Celtic.
A needless foul from Dougie Imrie on Leigh Griffiths brought Celtic a penalty, and the striker stepped up to slot home his 33rd goal of the season.
Dedryck Boyata was sent off for a last-man tackle on Accies’ Carlton Morris five minutes before the break.
Michael McGovern saved a second Griffiths spot-kick, and Brophy’s powerful strike rescued Accies a point.
They move above Motherwell into ninth in the Premiership table, two points above the relegation play-off place currently occupied by Kilmarnock.
Celtic extend their cushion at the top of the table to seven points, but Aberdeen can take advantage of the champions’ slip-up by closing the gap back to four points when they host St Johnstone on Saturday.
Hamilton were a world away from January’s humiliating 8-1 thrashing at the hands of the same opponents, and very nearly took the lead through Ali Crawford.
Scott Brown lost out to Morris who put in Crawford though on goal, but he shot over the bar when he really should have scored.
Accies had settled into the game after an dominant opening period from the visitors, but fell behind due to a moment of madness from Imrie.
Griffiths was in possession but in an unthreatening position and only Imrie will know why he sent the Celtic striker crashing just inside the area.
The striker took the penalty himself and fired the ball right down the middle.
It was a crazy moment from Imrie, a point Mikey Devlin was presumably making as he squared up to his team-mate in the wake of incident.
But suddenly the game was alight.
Boyata was sent off for a tackle on Morris. He tried to play the Accies striker offside but mistimed his movement and the forward was in on goal.
The lunging challenge ended a clear goalscoring opportunity just outside the box, but the Celtic bench – and their support in a crowd of 5,017 – clearly felt the tackle was legitimate and the defender had touched enough of the ball.
Manager Ronny Delia immediately reshaped his 10 men, replacing the returning Kris Commons with Charlie Mulgrew.
The flames continued to burn in the second half. Gary Mackay-Steven was through one-on-one with McGovern but could not finish, and Griffiths saw a clever effort fly just past the post.
Then came another moment of controversy and another penalty. Ziggy Gordon was spotted wrestling with Mikael Lustig at a corner and referee Craig Thomson pointed to the spot.
Again Griffiths stepped up, but this time McGovern produced a fine, diving save to keep the outcome in the balance.
It was a costly miss because minutes later home boss Martin Canning introduced Brophy – criticised by some after celebrating his goal in the recent thumping at Parkhead – and the substitute had the desired effect.
Celtic failed to deal with a corner and when the ball dropped in the box to Brophy he smashed a finish high into the net to ensure honours were even at the end of a pulsating match.
Infantino is a 45-year-old lawyer from Brig in the Valais region of Switzerland, less than six miles from Blatter’s home town of Visp.
He entered the presidential race when it became clear that Michel Platini, boss of European football’s governing body Uefa, could not stand.
“I will work tirelessly to bring football back to Fifa and Fifa back to football,” he said. “This is what we want to do.”
He added: “I feel a lot of emotion and have not realised yet what has happened today. It is still very fresh and it’s been a long and exciting journey and I probably need some time to chill out and see what has happened.”
The election was due to be fought between five candidates, but South African Tokyo Sexwale withdrew before voting began in Zurich.
The first round of voting failed to determine an outright winner, though Infantino led with 88, three more than pre-vote favourite Sheikh Salman.
A simple majority of more than 50% – 104 of 207 available votes – was sufficient for victory in round two.
Not since 1974, when Joao Havelange of Brazil beat 13-year incumbent Stanley Rous of England, has a second round been needed.
What will Infantino do now?
An emotional Infantino told delegates that together they would “restore the image of Fifa and the respect of Fifa”.
He added: “I want to work with all of you together in order to restore and rebuild a new era of Fifa where we can again put football at the centre of the stage.
“Fifa has gone through sad times, moments of crisis, but those times are over. We need to implement the reform and implement good governance and transparency. We also need to have respect.
“We’re going to win back this respect through hard work, commitment and we’re going to make sure we can finally focus on this wonderful game.”
Has he been well received?
Gary Lineker, an outspoken critic of Fifa and former president Blatter, wished Infantino “all the best” following his appointment.
The former England striker added on Twitter: “He’s got one hell of a job on his hands but seems a decent chap. Needs a sizeable new broom.”
The television presenter then joked: “Have this weird feeling that Gianni Infantino will pull off his mask to reveal Sepp Blatter.”
Portuguese great Luis Figo added his congratulations, tweeting: “Finally the change arrived. It’s time for a new era in Fifa.”
English Football Association chairman Greg Dyke said: “He is not a politician and he is not an ego. Fifa has been dominated by egos for a very long time. He is the type of person who will just get on with the job.”
Russian sports minister Vitaly Mutko said: “I am happy. We supported him from the start. World football needs such a pragmatist.”
German football federation interim president Rainer Koch said: “We are happy and relieved with Gianni Infantino’s victory and the fact that European football will continue to have a strong influence.”
Norway’s Karen Espelund, a member of Uefa’s executive committee, added: “We needed someone credible, we needed a clean winner, a clean man. I believe we have that in Gianni.”
International Olympic Committee president Thomas Bach said he was looking forward to working with Infantino for “the sake of sport”.
US Soccer president Sunil Gulati tweeted: “Congratulations. We look forward to working together to embrace reform and good governance.”
Has Blatter reacted?
Yes, the 79-year-old issued a statement after the election. It read: “I congratulate Gianni Infantino sincerely and warmly on his election as the new president.
“With his experience, expertise, strategic and diplomatic skills he has all the qualities to continue my work and to stabilize Fifa again.”
What now for Fifa?
Infantino has a hard job resurrecting its fortunes after a number of damaging episodes in the organisation’s history.
Criminal investigations in the United States and Switzerland have resulted in the indictment of dozens of football officials for corruption, many of them serving or former presidents of national or continental associations.
Swiss authorities are reviewing more than 150 reports of suspicious financial activity linked to those awards and said they had sent more documents, including an internal Fifa report, to US investigators.
So will we see change?
That’s the “big question” says BBC sports editor Dan Roan. “Fifa came into today very much on the brink, its future on the line,” he added.
“If it failed to elect the ‘right man’ and failed to pass the reforms needed, then the calls for it to be wound up would have become impossible to ignore.
“Many of those in the game will be breathing a sigh of relief. But it’s important to remember Infantino is a football insider himself. He has close links with a disgraced power-broker in Platini.”
What else happened in Zurich?
To help the new president tackle the crisis enveloping Fifa, key reforms were passed to help make it a more transparent and accountable organisation.
All salaries of Fifa officials will be disclosed, while a limit of four years has been placed on a president’s term.
A new council to replace the current executive committee has also been introduced, featuring a female representative from each confederation.
Dyke said the reforms were “more important” than the new leader.