Leverkusen's Afghan midfielder Nadiem Amiri was booked on 90 minutes and had to be restrained after the final whistle during a heated exchange with a group of Union players.
"Nadiem Amiri's background was insulted. There is no place for that on the pitch here. That is the saddest thing about the whole evening," Leverkusen defender Jonathan Tah said.
Tah said he heard the insult "shitty Afghan" aimed at Amiri and wants Germany's football governing body to investigate, adding: "I hope there are consequences."
The incident threatens to cast a shadow over Union claiming another major Bundesliga scalp at home, four weeks after an upset win over Borussia Dortmund.
Having hit the post earlier, Union's replacement forward Cedric Teuchert sprinted onto a pass which split Leverkusen's defence and fired home winning goal two minutes from time.
The 24-year-old made amends for squandering a golden chance six minutes after the break when his shot beat Lukas Hradecky, smashed the post and rolled agonisingly along the goalline and away to safety.
"I don't think any teams like playing us here and it's a lot of fun playing in this team at the moment," said match-winner Teuchert.
On top of the allegations of racism against Union, the victory could have come at a cost as Teuchert replaced Dutch striker Sheraldo Becker, who was helped off on 24 minutes with an ankle injury.
On Saturday, RB Leipzig can go top of the table if they beat Wolfsburg.
A Leipzig win would bridge the two-point gap behind embattled leaders Bayern Munich, who host Freiburg on Sunday.
Bayern are under pressure after last weekend's league defeat at Borussia Moenchengladbach and the midweek German Cup exit at second division Holstein Kiel.