Verplank, who had a strong personal relationship with Nelson, rose 37 places thanks to his fifth win on the PGA TOUR and his first since the Canadian Open in 2001.
Tiger Woods will return to action this week at the Wachovia Championship and stayed in first for the 441st week. Jim Furyk, last year's winner of the Wachovia, remained in second.
Phil Mickelson tied for third at the Byron Nelson and switched places with Adam Scott. Mickelson is third this week, followed by the Australian and Ernie Els.
Henrik Stenson and Vijay Singh held their places from last week with Stenson getting sixth and Singh seventh. Reigning U.S. Open champion Geoff Ogilvy climbed to eighth, while two-time U.S. Open winner Retief Goosen fell to No. 9.
Luke Donald took second behind Verplank and moved up one to round out the top 10.
Padraig Harrington fell one to 11th, followed by Trevor Immelman, Paul Casey, Sergio Garcia and Masters champion Zach Johnson, all of whom stayed in the same places as last week.
Charles Howell III and Nick O'Hern remained in 16th and 17th, respectively. Rory Sabbatini also tied for third and moved to No. 18. David Toms and Stuart Appleby completed the top 20.
Charl Schwartzel won the Open de Espana on the European Tour and jumped up 18 spots to No. 40.