We've confirmed ... Aguilera and Matt Rutler had a late-night dinner date at Mario Batali's restaurant Osteria Mozza ... where they hung out in the private dining room past midnight.
We're told one of the restaurant patrons recognized Christina and asked the server to send her a drink ... but the server replied, "She's already drinking a bottle of wine... or two."
The patron sent over a dessert instead.
So far, no word on when Aguilera and her BF left the joint -- but sources who were at the restaurant tell us the couple got their entrees AFTER midnight ... when the place was closing down to the public.
As TMZ first reported, the couple was arrested around 2:45 AM this morning -- cops say Matt was driving drunk and Xtina was too drunk to take care of herself.