Burglars struck the L.A. home of Lakers star Nick Young last night ... WHILE THE LAKERS WERE PLAYING ... TMZ Sports has learned.

Law enforcement confirms ... cops are investigating at the home Nick is renting in L.A.

Sources tell us ... Nick came home after defeating the Orlando Magic at Staples Center around 11pm and noticed an upstairs window was broken.

We're told the scumbag (or scumbags) ransacked the master bedroom -- taking several expensive items ... including Louboutin shoes, jewelry, clothes, Louis Vuitton luggage and more.

Our sources say they believe the crooks were so bold, they walked right out the front door ... which was unlocked when Nick got to his home.

So far, cops say no arrests have been made and no suspects have been identified.