It all went down Tuesday night during the 2nd period of the Predators vs. Red Wings game -- when ref Tim Peel blew the whistle on Predators forward Viktor Arvidsson for tripping Jon Merrill.

It sure seems like Merrill flopped -- even the announcers commented, "That's such a dive" -- but Peel seemed locked in on calling Arvidsson for the penalty anyway.

Moments later, a hot mic captured referee Tim Peel explaining why he made the call ... and his explanation is troubling.

"It wasn’t much," Peel said of the tripping penalty, "but I wanted to get a f***ing penalty against Nashville early in the ..."

The audio trails off before Peel completes his thought -- but it sure sounds like Peel had out it out for Nashville, which is a huge problem for the NHL. Refs are NOT supposed to have an agenda when it comes to calling a game.

The NHL immediately launched a probe into the remarks ... and it took just hours before the league formally fired the 53-year-old ref.

The league didn't hold back in explaining the decision either ... saying straight up there was "no justification for [Peel's] comments."

"Nothing is more important than ensuring the integrity of our game," league exec Colin Campbell said in a statement.

"Tim Peel's conduct is in direct contradiction to the adherence to that cornerstone principle that we demand of our officials and that our fans, players, coaches and all those associated with our game expect and deserve."

Peel had been reffing in the NHL for more than two decades ... and had been reportedly set to retire after his scheduled final game late next month.

As for the impact of the penalty ... it didn't seem to affect the Preds much -- they still went on to win the game over Detroit, 2-0.

Now, the big question ... why did Peel want to penalize Nashville -- and did he unfairly target other teams during his career???