Tampa Bay won its fourth in a row and has captured 10 out of 11.
James Shields (5-0) became the first five-game winner in the majors this year, striking out 11 over six innings and surviving two homers by Kyle Seager.
Seager hit a solo homer in the first and tied it up at 4-4 in the sixth with a three-run blast.
Scott then led off the bottom of the inning by driving a home run to center on a 3-2 pitch from Blake Beavan (1-3).
Seattle put runners on first and third in the eighth, but Joel Peralta came on to end the threat and then worked a perfect ninth for his first save. It was Seattle's fifth straight loss.
Shields has won five consecutive starts for the first time in his seven-year career.