Sources close to the couple tell TMZ ... Faith placed a call Tuesday around 6 PM to a local minister, named Joelle Righetti, asking if she was available to do a wedding at Trump Hotel, stat.
Righetti refers to herself on her website as the "Gypsy Mobile Minister."
As we first reported ... the couple was spotted Tuesday outside a Vegas courthouse where they got a marriage license. A little less than 5 hours later -- around 10:30 PM -- the ceremony went down.
The ceremony was performed in the living room of their hotel suite with Faith and Stevie overlooking the Vegas strip. Sources close to the couple tell us they held hands and teared up while "Ave Maria" played on a portable speaker.
We're told the "Gypsy Minister" -- whose services cost a couple hundred bucks -- had no idea she was marrying off celebs. She even asked Faith if she was a model or an actress. Faith politely said she's a singer ... to which the minister said, "Me too!"