Tway climbed to No. 45 this week and added his name to the growing list of players over the age of 40 to win on the PGA Tour in 2003.
Tiger Woods remained in first place for the 213th consecutive week, followed by Ernie Els, who cruised to a six-shot victory at the European Masters. Davis Love III, Vijay Singh and Jim Furyk rounded out the top-five.
Masters winner Mike Weir finished 10th at the Canadian Open and held on to the sixth spot. David Toms, Kenny Perry, Padraig Harrington and Phil Mickelson all stayed put this week and completed the top-10.
Nick Price kept the 11th ranking, while Retief Goosen, Darren Clarke, Justin Leonard and Chris DiMarco each remained in their positions from last week's rankings.
Robert Allenby and Sergio Garcia held on to the 16th and 17th spots, respectively. Jay Haas moved up one to 18th, while Adam Scott, last week's Deutsche Bank Championship winner, fell one to 19. Thomas Bjorn came back into the top-20 this week while Rocco Mediate fell one to 21st.