They went ahead with an operation to try to save the healthy baby, but his brother refused to die, surviving two termination attempts during the procedure.
Now, Gabriel and Leuan Jones are 7-months-old, and healthy.
Doctors have nicknamed Gabriel "Rocky," for his fierce determination.
According to the London's Daily Mail newspaper, Gabriel had an enlarged heart, and physicians thought he'd die in utero, and that Leuan would also die as a result.
Doctors first tried to cut Gabriel's umbilical cord, but it was too strong. They then cut Rebecca's placenta in half, so Gabriel's eventual death wouldn't affect Leuan.
But, somehow, Gabriel lived on, even though he weighed less than a pound at the time.
The babies were delivered by caesarean section five weeks later.
On The Early Show Tuesday, Rebecca told co-anchor Hannah Storm their decision "was really, really difficult, but I guess, at the end of the day, we had to decide whether we wanted to go through the pregnancy and come out of it with no babies at all or just one of them."
Gabriel's death, she and Mark were told, was imminent.
"In reality," Rebecca continued, "it was a decision that was quite easy to make, because we desperately wanted both of them," but didn't think they would have either of them."
Gabriel, she explained, had "stopped growing. His body was just shutting down, and he was actually dying. And, because they were identical twins, it was a very, very high-risk that we would lose both of them when he did die."
So she and Mark gave the go-ahead for the termination surgery.
"We just expected to not see him the following morning," she continued, "but, the following morning, when I went for a scan and Mark came in, I said, 'He's still there, and I know he's still there!' And he just continued to grow. But we actually never gave up, because we wanted to both of them so desperately."