Babe Ruth -- SIX-FIGURES for Ultra-Rare Baseball Cap ... Original Jordans Auctioned Too

Babe Ruth's game-worn baseball cap from a 1934 barnstorming trip to Japan just hauled in an amazing $303,277 in an auction ... TMZ Sports has learned.

No, it's not gold-leafed or anything, but it did sit on the Babe's skull while he did some diplomatic work for the U.S. He was part of an American all-star team sent to Japan in 1934 to play 18 exhibition games.

The games were supposed to ease rising tensions between the U.S. and Japan, but failed. See WWII.

We're told the ball cap remained with the Ruth family until 30 years ago ... then changed hands twice ... before landing on the block this morning at Grey Flannel Auctions.

Another sports legend fetched big dollars too -- an original pair of Jordan's ... just not Air Jordans.
The CONVERSE shoes MJ wore during his '81-'82 season at UNC went to the top bidder for $33,378!

We're told the winning bidders on both items want to remain anonymous.