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"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
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