Luke Donald regained top spot in the world rankings from Rory McIlroy after finishing third in the Zurich Classic of New Orleans.
The Englishman needed a top-seven finish to move back to the head of the standings and a final-round 67 saw him finish third, two shots adrift.
American Jason Dufner beat Ernie Els in a play-off for his first PGA Tour title after they finished tied on 19 under. Masters winner and defending champion Bubba Watson carded 70 to end tied 18th at 11 under.
The world number one spot has changed hands nine times in the last 18 months, with Tiger Woods, Lee Westwood and Martin Kaymer also holding the position. With Donald absent this week, McIlroy can regain top spot in the Wells Fargo Championship in North Carolina.
"It's been going back and forth a little bit. Rory's turn next week. It was a little bit of a motivation to try to play well today," said Donald on Sunday.
Dufner took a two-shot lead into the fourth round but his two-under 70 was not enough to hold off Elss 67.
Both missed birdie putts within eight feet on the par-five 18th on the first play-off hole, but Dufner holed a short birdie putt and Els missed one from the fringe on the 18th for a second time to hand the 35-year-old a first title in 164 starts on the PGA Tour.
Dufner lost play-offs last year to Mark Wilson in the Phoenix Open and Keegan Bradley in the US PGA Championship for two of his three career runner-up finishes.
"To get the monkey off of my back, it's a great feeling," said Dufner, who is getting married next weekend.
Three-time major winner Els last won on the PGA Tour in the 2010 Arnold Palmer Invitational at Bay Hill. "It was a nice little charge I made and, you know, nice to catch the leader," said the South African.
"I had a chance to win the tournament with a six-footer and missed it, but I made quite a few putts on the back nine to keep myself in it."
Defending champion Watson, playing for the first time since his Masters win over Easter weekend, entered the final round eight shots off the lead and was unable to mount a charge after bogeys on his first two holes.
"All in all, pretty good week being tired, coming back for the first time after winning the Masters, all this different media attention," Watson said.
"It's something you got to get used to. It wears on you, tires you out. Somehow I finished - I'm in the top 20. A lot of guys wished they did that."
ZURICH CLASSIC FINAL-ROUND LEADERBOARD (US UNLESS STATED)
-19: J Dufner, E Els (SA) [Dufner wins after play-off] -17: L Donald (Eng) -16: R Palmer, G DeLaet (Can) -15: S Stricker
Selected others: -13: J Rose (Eng) -11: B Watson -9: G Owen (Eng)
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