Jane Hitchens and Nik Brbora, both from England, were transported to the U.S. Coast Guard Cutter Bertholf. It was too dangerous to airlift them by helicopter so they were picked up by a small boat.
Hitchens, a 50-year-old doctor, has suspected broken ribs and is being treated with oxygen. Brbora, 29, is suffering from a suspected pelvic strain.
They will be transported from the Coast Guard ship to a hospital in San Francisco by helicopter.
Four crew members of the nearly 70-foot Geraldton Western Australia were injured after large waves swept away the yacht's steering mounting and some communications equipment on Saturday.
The Coast Guard launched a helicopter early Sunday evening to rescue the sailors. The plan was for the helicopter to hover above the damaged boat and lower rescuers onto the deck to help the four injured crew members.
Weather conditions were an issue all day, with choppy seas, high winds and large swells hampering the effort.
Rough conditions move the sailboat back and forth which makes it more difficult to evacuate the injured, according to Lt. Charlie Kelly of the U.S. Coast Guard.
"The weather is always unpredictable. The risks are always out there. They will do their best to mitigate them," Kelly said.
Another Briton, 47-year-old Mark Burkes, and 62-year-old Australian Max Wilson, were also hurt aboard the racing yacht.
The yacht is about a few hundred miles from the Bay Area. It was sailing toward the Golden Gate to meet other vessels competing in the Clipper 11/12 Round the World yacht race when stormy conditions hit.
Saturday night a C-130 crew from Travis Air Force Base was able to drop supplies to the yacht crew, but stormy weather prevented rescuers from reaching them.
-- ABC7's Lilian Kim contributed to this report.