Anthony Davis -- 21st Birthday Shocker ... Huge Party, No Booze

Anthony Davis did the unthinkable for his 21st birthday ... he woke up WITHOUT a hangover -- TMZ Sports has learned the NBA superstar didn't take a single sip of alcohol at his b-day party.

Davis celebrated the big 2-1 on Tuesday ... and to celebrate, his friends and teammates threw him a party at Desi Vega's Steakhouse in New Orleans on Monday night ... before hitting a local sports bar called Walk-Ons.

We're told 95% of Anthony's New Orleans Pelicans teammates attended -- along with his friend (and fellow Red Bull endorser) Lolo Jones.

But when the clock struck midnight, and Davis was legally allowed to booze ... we're told Anthony stuck with iced tea and sodas -- and told employees he was serious about sobriety because he wanted to be fresh for practice in the morning.

Pretty mature for a 21-year-old.

Fun Fact -- We're told New Orleans rap legend 5th Ward Weebie also came out to Walk-Ons and performed at Anthony's party ... and even led the crowd in a rendition of "Happy Birthday."