The Croatian, who only joined the Berlin team in November, received a blatant red card for pushing Sane in the face twice during their 1-0 Bundesliga defeat against Bayern Munich.
With just over 15 minutes to play, Sane tried to claim the ball from the coach on the touchline, but Bjelica pulled it away from him.
The former Manchester City man then swiped his hand at the ball, before the pair squared-up and Bjelica quite clearly pushed him in the face twice.
Players quickly came to break up the fracas, with Eric Dier acting as peacemaker during his first minutes for his new team.
Referee Frank Willenborg had no other option but to send off the manager, but that wasn't the end of the story.
read more bundesliga news
Forgotten ex-Southampton man betters Kane in key Bundesliga goal stat
Bayern and Kane fall seven points from Bundesliga lead as fans turn on Tuchel in defeat
The 52-year-old continued arguing on his way up to the executive boxes, and seemingly hit out at Bayern fans on his way, and had to be calmed down by staff members.
It was a match Union went onto lose 1-0 with Raphael Guerreiro scoring the winner in the opening seconds of the second half.
The result means Bayern are now four points behind Bundesliga leaders Bayer Leverkusen having played the same number of games.
Even with three points on the board, it wasn't an entirely inspiring performance from the champions after their damaging defeat to Werder Bremen last time out.
Most read in Bundesliga
Harry Kane or Kingsley Coman record will end as Bayern's season hangs in the balance
History could repeat itself to help Harry Kane win first ever trophy at Bayern Munich
Souness makes Kane 'catalyst' claim with Bayern Munich keen on Trippier
Forgotten ex-Southampton man betters Kane in key Bundesliga goal stat
That makes Bjelica's complete loss of control all the more bizarre, with Union only a goal down and in with a chance of an upset before losing him.
Asked why he reacted in such a way post-match, Bjelica said: "I'm not reacting the way I should react as a coach. That's not okay and what I did shouldn't be tolerated.
"I'm in my zone, I want to get the ball and give it to Sane. He comes into my space pushed me, then of course I reacted. He comes into my space to provoke me."