That year he won the Shearson Lehman Brothers Andy Williams Open, Manufacturers Hanover Westchester Classic, Georgia-Pacific Atlanta Golf Classic, and the PGA Championship. He also won the PGA Player of the Year award that year. In 1989 Tway won the Memorial Tournament and the next year he won the Las Vegas Invitational. He won the MCI Classic in 1995 and the Bell Canadian Open in 2003. In 1986 and 1987 Bob spent 25 weeks in the top 10 of the Official World Golf Rankings. He finished 3rd at the U.S. Open in 1998, 5h at The Open Championship in 1991, and 8th at the Masters Tournament in 1986. Tway won the PGA Tour Comeback Player of the Year award in 1995. Tway joined the Champions Tour in 2009.