Archer (6-3), won his fourth straight start and posted his second whitewash in three outings, yielding only a fifth-inning single to Lyle Overbay and a ground-rule double to Brett Gardner in the sixth.
The rookie right-hander didn't issue a walk and struck out six for the American League East-leading Rays, who improved to 19-3 in July.
Kelly Johnson provided the game's only run with an RBI single in the sixth.
New York's Ivan Nova (4-4) took the hard-luck loss, surrendering just the one run on six hits over seven frames. He walked three and fanned eight.
The fourth-place Yankees fell eight games behind Tampa Bay in the East..