The low-key couple, who have yet to make a red carpet appearance together, had primo seats right behind home plate.
And although they tried to go incognito in their hoodies, fellow sports fans noticed that "they were holding hands and kissing throughout the entire game."
And Shia was quite the gentleman to his girlfriend...
Our source says when Mulligan got cold early in the game, LaBeouf gave her his sweatshirt and ran to the concessions to buy a new one for himself.
"Shia was originally wearing a gray sweater, but when Carey got cold he immediately took it off and gave it to her," says our source. "It was very sweet."
The cute couple was seen playfully singing along to "Take Me Out to the Ball Game" during the seventh-inning stretch and snacking on nachos, ice cream sandwiches and sodas.
Too bad all that adorable affection didn't translate into good luck for the home team—the Brewers beat the Dodgers, 11 to 3.
See more famous fans in our Dodger Dawgs gallery!