I was following it on the scoreboard and I'm pretty sure Katie had 40-15 (at 5-4 up) so I'm presuming she actually won it 6-4 in the third. I looked at the completed matches and it's not the only match to be done as 5-something.
She's off the live score but completed matches says the score was 1-6, 6-1, 5-4. Maybe the other girl retired?
Katie led 40-15 and then it just disappeared, so have to presume that she won that point to win or the match (or her opponent was a really bad loser and retired at match point... making sure that Katie didn't have a chance to choke)
Good win... but losing the first set wasn't the smartest idea