We just got Yankees manager Aaron Boone rushing to Yankees Stadium for Tuesday night's big game against the Boston Red Sox -- and he was cool enough to talk to our guy!!!

The big talk -- the rivalry ... which has gotten more intense this season for two reasons -- the Yanks and Sox have the best records in baseball PLUS the teams got into a brawl the last time they faced off in April.

So, with pride and 1st place on the line ... how does Boone feel about the situation?

"It's always big when these two teams get together," Boone said.

"They're a great team. We think we have a good team ... so it's fun to be a part of."

As for concerns that tonight could get violent?

"Nah, all good ... hopefully we'll just see a lot of good baseball."