Mr. New York State of Mind put on a show for a sold-out crowd at Madison Square Garden Thursday night -- the 64th time he's done so -- but this concert happened to coincide with the legendary musician's bday.

So, his oldest daughter, Alexa Ray, made sure her big shot dad didn't get away without a song sung in his honor ... and brought out Billy's 3-year-old daughter, Della Rose, with her for the occasion.

Pretty sweet moment, and it even includes the awkward "... happy birthday dear Billy/Dad" confusion that almost always happens when you sing the song to a family member while surrounded by 20,000 friends.

Classic.

And, in case you're wondering ... Alexa is Billy's first child from his marriage to Christie Brinkley. He also has 2 daughters with his current wife, Alexis Roderick -- Della and 1-year-old Remy Anne.

Remy didn't get any stage time ... but we're sure Joel will have many more MSG shows to make it happen.