Karl-Anthony Towns' birthday dinner wasn't short on booze ... 'cause the NBA star was sippin' on some good stuff throughout the night -- including a cognac that comes with an insane price tag!!
The Timberwolves star was surprised by his family and friends when he arrived at a venue with his longtime girlfriend Jordyn Woods on Tuesday -- his 27th birthday.
The place was decorated nicely for the occasion ... from a massive "27" sign to a ton of balloons and sparklers -- and a birthday cake featuring his T-Wolves jersey.