Moore (13-3), who struck out 10 in 7 1/3 innings, kept the Twins hitless through 5 2/3 innings before Brian Dozeri doubled and scored on Jamey Carroll's single. No pitcher in the majors has more than 13 wins so far this season.
The home runs by Scott and Longoria came off Minnesota starter Mike Pelfrey (4-7) in the sixth inning and put the Rays ahead 3-1. Tampa Bay added another run in the seventh.
Minnesota, however, strung together a two-walk, two-single rally that ended with Joe Mauer's two-run base hit, pulling the Twins within 4-3.
Joel Peralta was brought in at that point and got the final out of the eighth and Jake McGee pitched a 1-2-3 ninth -- striking out the last two Minnesota batters -- for his first major league save. The Tampa Bay pitchers only allowed four hits between them. Moore allowed three hits.