Lowery is up to 116 in the world.
Tiger Woods remained comfortably in first, followed by Phil Mickelson, Steve Stricker, Ernie Els and Adam Scott.
Jim Furyk, Justin Rose, Rory Sabbatini and K.J. Choi stayed in their spots from last week. Singh, who blew a three-shot lead on the back nine, moved up one to 10th.
Reigning British Open champion Padraig Harrington slipped to 11th, while Sergio Garcia and Henrik Stenson held on to 12th and 13th, respectively. A pair of former U.S. Open champions switched rankings this week with Angel Cabrera jumping to 14th and Geoff Ogilvy slipping to No. 15.
Masters winner Zach Johnson, Aaron Baddeley, Lee Westwood, Luke Donald and Trevor Immelman rounded out the top 20.