I won a sheet of stamps with the New Year's greeting card you sent me.
The New Year's greeting card you gave me had a winning number on it. I got a free set of stamps.
この場合、次のような言い方ができますよ。
ーI won a sheet of stamps with the New Year's greeting card you sent me.
「あなたが送ってくれた年賀状で切手シートが当たりました」
to win ... with the New Year's greeting card you sent me で「あなたが送ってくれた年賀状で…が当たる・当選する」と言えます。
ーThe New Year's greeting card you gave me had a winning number on it. I got a free set of stamps.
「あなたからもらった年賀状は当選していて、切手が当たりました」
The New Year's greeting card you gave me had a winning number on it. で「あなたからもらった年賀状が当選していた」と言えます。
ご参考まで!