Rangers had been leading through Daniel Candeias’ strike just before the break as Steven Gerrard’s side look to close the gap at the top of the Scottish Premier League.
But the headlines will follow the shocking incident that happened on the brink of half time.
Tavernier was on the touchline trying to collect the ball ahead of a throw-in when the incident happened.
As the TV footage shows, a Hibs fan clambered over the advertising hoardings and tried to kick the ball away from Tavernier.
He then shoves the Rangers player and confronts him, before police drag the spectator away.
Ally McCoist and Alan Stubbs were summarising the match for BT Sport.
And the two former footballers were not impressed by what they saw.
“I don’t know what he’s doing, I really don’t,” McCoist said.
The fan climbed over the advertising board to confront Rangers star James Tavernier
The fan proceeded to kick the ball away from the Rangers captain, who then approached the man
Rangers captain James Tavernier moved towards the unidentified fan
That is a complete and utter imbecile
“He runs by the security guard. I think initially he tries to kick the ball.
“But make no mistake about it, that is a complete and utter imbecile.
“And with a bit of luck he will be spending at least a night in the cell.
Stubbs then said: “It’s just so sad to see because it’s just mindless individuals.
“You’ve got to be careful though not to tar the same brush to all the fans.
“But it’s the minority of some idiots who are trying to spoil everything.
Hibs fans FIGHTS with Rangers star James Tavernier
The Hibs fan jumps over the advertising hoardings
“You look at Hibs fans, Rangers fans, Celtic fans – you go through them all – and they’re a great set of supporters.
“But you’ve always go the mindless idiots who are going to spoil it for everyone else.”
McCoist then referenced the incident last week when a bottle was thrown at Celtic player Scott Sinclair.
“And particularly what’s happened in the last week or so. It’s crazy, crazy,” McCoist said.
The Hibs fan can be seen running along the touchline
Hibs CEO Leeann Dempster said: “I’m was going to call him a supporter, but I’m not going to call him a supporter.
“It’s just unacceptable, completely unacceptable. This week alone we’re had to write to Scott Sinclair and apologise to him for the bottle (thrown at the Celtic player).
“Now I have to go and see Mr Tavernier and apologise to him as well. It’s unacceptable.
“A statement on the club website is not enough, we have to talk about this.
“It reflects badly on the club, it reflects badly on the whole Scottish game.
“Actually the Scottish game is thriving – it’s doing lots of good things.
“But what do we talk about again tonight?
“We talk about an absolute foolish idiot. Coming onto the pitch is completely unacceptable.”
Leeann Dempster brands the Hibs fan an “absolute foolish idiot”
Leeann Dempster says Hibs will apologise to James Tavernier
The incident comes after Rangers chairman Dave King and manager Steven Gerrard condemned the actions of a minority of their supporters for alleged sectarian chants, in a turbulent week for Scottish football.
A club statement read: “Rangers Football Club takes this opportunity to remind fans of the need to support the team in the correct manner.
“As the manager, Steven Gerrard, strives to provide excellence on the pitch, we, the support, must also strive to protect the club and ensure that Rangers is projected in the best possible light.
James Tavernier can be seen berating the Hibs fan
“The majority of our supporters recognise that they are the club’s ambassadors and that unacceptable behaviour has no place in our ranks.
“Let’s not give anyone a chance to criticise this great club, your club.”
Another incident in a difficult few weeks for football in the country also took place this week after Brendan Rodgers saw his house burgled after he left the Celtic to join Leicester City.
Rodgers had his medals stolen in the incident, and speaking for the first time since, he was asked whether he would try to replace the stolen medals.
James Tavernier pushed the fan before stewards removed him from the ground
“Yeah, I’ll just have to try to get some more,” he said with a smile.
“It’s obviously something that’s not nice for any family to go through.
“As I said it gave the girls a fright.
“The last ten days there’s been a lot of talk about my move to here. I don’t want to detract from an amazing time we had in Glasgow.
“The experiences we had there were amazing on and off the field. We don’t want to let the last 10 days cloud any of that.”