The former US Open champion remains at the top of the latest rankings, holding a slender lead over Justin Rose and his fellow American Brooks Koepka.
Johnson took a one-shot advantage into the final round on Sunday, before making four bogeys and two double-bogeys to drop to a tie for 28th.
Taiwanese golfer Pan Cheng-tsung climbed 58 places to 55th after taking advantage of Johnson's meltdown to clinch his maiden PGA Tour title.
Tiger Woods remains sixth in the rankings after not playing the week following his stunning fifth victory at the Masters.
World top 20