Rivaldo, 36, signed for the team last week. The club - founded just three years ago - is reported to be paying the former World and European player of the year $14 million over a two-year contract.
The player signed for Bunyodkor despite having a year left on his contract at Greek club AEK Athens.
"I ask forgiveness from AEK supporters, but you can't say no to such a proposal," Rivaldo told a Greek radio station after the club had given him permission to leave.
"I had to make a very difficult decision. Something very positive has come up late in my career and I cannot turn it down," he added.
The 2002 World Cup winner could not have hoped for a better start to his Uzbek adventure, scoring both the goals as his side beat Mashal 2-0 away from home. The first goal came in the 11th minute, when the attacking midfielder hammered a shot into the corner of the net. With a minute to go, another shot from the edge of the area saw Rivaldo claim his second, and all three points for Bunyodkor.
In July, Bunyodkor claimed to have secured the signature of Barcelona's Samuel Eto'o. The club was reported to have offered the player some 30 million for two years. However, despite the Cameroonian star visiting Tashkent, the Uzbek capital, for talks, the deal failed to go through.
Rivaldo's new club was founded in 2005 as Kuruvchi, which means "builder." The club changed its name last month to Bunyodkor, which means "creator."
The side, which is now eight points clear at the top of the domestic league, boasts a number of Uzbek energy companies as sponsors.
