Cameron Mack, 21, climbed over the advertising hoarding at Easter Road and kicked the ball away from the defender.
He pleaded guilty to breach of the peace at Edinburgh Sheriff Court on Monday and will be sentenced next month.
He has been banned from all football matches in Scotland.
Mack, from Port Seton, admitted acting in a disorderly manner, kicking the ball away, approaching Tavernier and acting in aggressive manner.
The court heard both men pushed each other several times before a steward and police intervened.
Defence solicitor Stuart Carson said his client had no previous convictions and asked for bail.
Sheriff Adrian Cottam agreed to the request, but said: “The nature of the offence has caused a lot of discussion and concern and is a serious matter.”
The Premiership match on Friday night finished 1-1.