Kate Hudson at New York's Citi Field
Storms Media Group
continued to follow her New York Yankees beau
Alex Rodriguez on the road Friday night, attending the opening game of the "Subway Series" at Citi Field in Queens, N.Y., against the New York Mets – where, in the eighth inning, A-Rod hit his 564th career homerun.
"Kate was standing and clapping and cheering during the game, especially when A-Rod hit a homerun," a source at the game tells PEOPLE. "She looked adorable and was so happy."
For the hunky ballplayer, 33, it was a milestone that pushed him into 11th place on the all-time homer list, one spot ahead of the legendary Reggie Jackson.
At the game – which the Yanks won, 9-1 – Hudson, 30, sat in the second row and her presence was anything but secret, as she frequently appeared on-screen over such sports cable networks as SNY-SportsNet NewYork.
As another source tells PEOPLE, "She's happy. She's having a great time with him."
Additional reporting by K.C. BAKER and LINDA MARX