In the final round, Warren overcame bogeys at the sixth and seventh holes to shoot 3-under 69. Karlsson, who carded a record 9-under 63 Saturday, shot only 1-under 71.
The players finished in a tie at 10-under 278.
"I don't seem to have any fear of what can go wrong," Warren said. "I've got the belief that under pressure I can conjure something up. Maybe I was born with it."
For his victory, Warren won $266,660.
Both players made bogey on the first playoff hole.
Peter Gustafsson (72) of Sweden and France's Raphael Jacquelin (70) tied for fifth at 7-under 281.