Archer (4-3) posted his first career shutout in his 13th major-league start with a 112-pitch gem. The right-hander didn't allow a walk and struck out eight in the dominating performance.
Desmond Jennings bashed a two-run homer and Kelly Johnson went 3-for-4 with two runs scored for the second-place Rays, who won for the 10th time in 11 games.
They came into the contest trailing American League East-leading Boston by 3 1/2 games.
Houston's Erik Bedard (3-6) took the loss, yielding three runs (two earned) on eight hits over five full innings.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys