"He's been sweeping her off her feet and courting her like a proper gentleman," a source tells PEOPLE of Baston, 45, the president of Televisa, the largest media company in Latin America. On Friday, he escorted the actress/producer, 38, to the Museo Jumex Opening dinner at Case De La Bola in Mexico City, Mexico.
Cameras flashed incessantly as the wealthy businessman and the former Desperate Housewives star made their way down their first red carpet together.
Last month, Longoria and Baston dined at New York's Serafina restaurant. A source told PEOPLE at the time that the Longoria was "very happy" with the budding relationship and that Baston was "crazy about her."