The bout went the full 12 rounds, with Parker finishing ahead on all three judges scorecards - 119-109, 115-113, 117-111 - to collect a unanimous points decision.
The former WBO world champion went into the fight ranked third with that organisation, while Fa was ranked fifth.
The fight was the first between the two South Aucklanders in the professional ranks. They fought four times in amateur boxing, winning two fights each.
Earlier, David Nyika started his professional career with a bizzare first round knockout win over Auckland's Jesse Maio.
The two-time Commonwealth Games gold medallist, who has qualified for this year's Tokyo Olympics, collected victory less than 30 seconds into the fight.
Nyika connected with an unintentional punch to the back of head as Maio ducked a right hook. Maio went to his kness before being counted out by the referee.