The Briton was dropped in the fourth round after Paul caught him with an uppercut – but the American landed another shot while his opponent was on the floor with the referee deducting two points.
It proved pivotal, with KSI securing a narrow in on the scorecards after six rounds of action.
On the undercard, Billy Joe Saunders marked his US debut with an underwhelming WBO super middleweight title defence against Marcelo Esteban Coceres.
The Briton laboured for much of the contest with boos coming down from the LA crowd before a thrilling finale.
Saunders produces two knockdowns in the 11th round – one a stunning uppercut that shook Coceres to his boots and while the Argentine was able to make the count, the referee stepped in to end it shortly after.
“No excuses but I only had five days preparation here and I knew from round nine that I had to get him out of there because everything was off, my timing and accuracy was all off.”