Investigating officers decided to search their cabin after crew members told them about a recent "altercation" between Rachid and Harris, the affidavit said.
When they arrived, they found Wilkinson holding what appeared to be drug paraphernalia, it said.
"Wilkinson then attempted to shut the cabin door on the officers while simultaneously opening the cabin bathroom door temporarily blocking the main cabin door.
"Agents heard the bathroom faucet turn on and observed Wilkinson rinsing what appeared to be drug paraphernalia in the sink."
Mr Hyatt said both Wilkinson and Harris were detained and removed from the cabin.
Agents then found keys in a light fixture which opened a suitcase inside the cabin, the affidavit said.
"Upon opening the black Pelican case, officers and agents discovered several packages of an unknown substance which later field tested positive for cocaine."
Both Wilkinson and Harris were arrested and charged with possession with intent to distribute more than five kilograms of cocaine.
A spokesman for the US. Attorney's Office in California said he would not comment on the ongoing case.
The Ministry of Foreign Affairs has confirmed it has offered consular assistance to the New Zealanders.
The MFAT spokesman would not say if they were in custody.
Wilkinson, Harris and Rachid were understood to have been aboard the Aurora during a world cruise and had arrived in San Francisco from Curacao, a Caribbean Island.
A P&O Cruises spokesman said he could not comment on an ongoing investigation.