Tiger Woods & Lindsey Vonn -- Holding Hands in Public!

Tiger Woods and Lindsey Vonn made their relationship red carpet official ... by holding hands at the Costume Institute Gala in NYC on Monday.

This is the sports super couple's first public display of affection since revealing they were bangin' by posting cheesy pics together on Facebook back in March.

In a glimpse of what may lie in their near future, Lindsey wore a virginal white gown as they walked down an aisle together.

Ironically, Tiger's next gig is competing in The Players Championship ... something he knows all about.