The actress and the Formula One driver were super flirty Tuesday after breaking bread together in New York City ... and the smiles on their faces tell the story here.

Seriously, look at these two ... Sofia and Lewis are grinning at one another from ear to ear and they seem absolutely smitten.

Flirty glances, playful gestures and two sexy, rich celebrities ... say no more!!!

Sofia and Lewis sat next to each other at a table by the window, and folks who were there say Sofia was so engaged in the conversation she barely touched her food.

They were joined by some friends but that didn't stop them from flirting outside the restaurant ... until Sofia climbed into the back of a black SUV and left.

Sofia's been drop dead gorgeous for decades and she's been playing the field for nearly a year since finalizing her divorce from Joe Manganiello.

She dated wealthy orthopedic surgeon Justin Saliman last year but was flying solo earlier this month at the Golden Globes, when she told Access Hollywood she's manifesting health, money and a lover in 2025.

Lewis famously dated Nicole Scherzinger back in the day and has been linked to tons of celebs since ... including, most recently, Shakira.