Casey, from England, switched places with Northern Ireland's Rory McIlroy and is now ranked No. 7, with McIlroy eighth.
Harrington, from Ireland, did the same with Sweden's Henrik Stenson, moving from 10th to ninth and sending Stenson the other direction.
The top of the rankings were unchanged. Tiger Woods, as he has been for 245 consecutive weeks, was No. 1, Steve Stricker was second and Phil Mickelson third. All are from the United States.
England's Lee Westwood was fourth and U.S. golfer Jim Furyk remained fifth with German Martin Kaymer in sixth.
Dustin Johnson, another American, won the AT&T Pebble Beach National Pro-Am and jumped 19 places to No. 25 in the world.
Copyright 2010 United Press International.