The Rays stayed out front in the race for the American League's second wild card spot. They own a 1 1/2-game advantage over both Cleveland and Baltimore and a two-game lead over the New York Yankees.
Archer (9-7) struck out seven and gave up three hits without a walk in six innings.
Desmond Jennings put the Rays in front with an RBI single in the second, a base hit by James Loney brought home another run in the third and Tampa Bay tacked on a score in the seventh when Yunel Escobar doubled home Jose Molina.
Kevin Correia (9-12) gave up all three runs on eight hits in six-plus innings to absorb the loss.