The Americans started strongly and never looked back in a 9-3 win over married Russian couple Bryzgalova and Krushelnitskiy in the first of seven rounds of preliminary play.
"Blood's thicker than water," Matt Hamilton said after the match.
Mixed doubles curling is one of four new events in the 2018 Winter Olympics and was the first to kick off official competition even though the Games do not formally open until Friday.
The Americans built a 3-0 lead in the first end when Becca Hamilton knocked two of the Russians' stones out of scoring position.
"Mixed doubles, you're never safe with a three-point lead, anyone can score big ends," Becca said.
The Americans never trailed after that first end and the game was called after seven ends when they had amassed an insurmountable lead.
The Russian duo, who became visibly agitated with each other following some missed shots, did not speak to media after the match.
The Americans' performance was not without its own awkward moments, however, as Matt Hamilton lost his balance as he was sweeping in front of a stone late in the match and fell heavily on to the ice.
He popped straight back up and finished the game with no visible difficulty.
"I've got more of a bruised ego than a bruised tail bone," he said.
(Editing by Greg Stutchbury)
