Have you read the Marvel SuperHero Vol. 2 #10-11? The first is the planned issue of Ms. Marvel that never saw print that was leading up to the events of Avengers Annual 10. #11 is essentially what you're asking about. It's from Mystique's point of view, but it does cut to Carol right after the incident with Marcus. She walked away from the Avengers because she believed they betrayed her. Mystique found her through Destiny.
As for how she was able to do it. Frankly, the art in the issue could have been clearer. It seems that she borrowed superstrength for the fight from someone else. Even then, Carol had the upperhand at first and carried Rogue to the Golden Gate Bridge. Once there, Rogue touched Carol and absorbed her powers and memories. I think it's because the issue is rushed, but the X-Men Animated Series has a better presentation. There, it's because she held on too long. The way it's shown in this issue, it looks like something just went wrong. I'll chalk that up to things being rushed and that time is a matter of how you perceive things in comics. It was a single panel, but we don't know how long that panel lasted.