The victory was Leonard's second in the Memphis tournament and his 12th on the PGA Tour.
Leonard, Immelman, the 2008 Master's champion, and Allenby tied at the end of regulation at 4-under-par 276.
Allenby shot 65, Leonard 68 and Immelman 69 in the final round at the TPC Southwind course.
"When I won here in 2005, I led every day and almost let it slip away at the end," Leonard said. "This week I was kind of back in the pack a little bit and was just able to shoot a really solid round today."
Leonard collected $1 million.