HBO's "Game of Thrones" prequel series took home the award for Best Television Series - Drama Tuesday night ... but as executive producer Miguel Sapochnik delivered his speech, most people's eyes were locked on Milly barely holding it together in the background.

You can see her giggling nonstop, having to hold on to costar Emma D'Arcy ... and giving some pretty wild expressions throughout Miguel's speech.

Twitter had a field day with Milly, with many calling her apparently boozy night "so funny."

Another spot-on description -- "When you don’t expect to win so you get drunk but you actually win and have to get on stage."

For those unaware, Milly plays the young version of Rhaenyra Targaryen in the series, and Emma takes over as the older version of the character after a time jump.

If Milly had been overserved last night ... good for her!!! The Globes have always been known as the Hollywood award show where celebs openly booze it up through the night -- and after a year in time-out (due to a lack of diversity at the Hollywood Foreign Press) -- it needed to come back with a bang.