Archer (3-3) allowed just one unearned run on three hits, didn't issue a walk and struck out two for Tampa Bay, which reeled off a sixth straight victory and 10th in 11 games overall.
Alex Torres and Jake McGee each tossed a scoreless relief frame and Fernando Rodney racked up his 21st despite allowing a pair of hits in the ninth for the second-place Rays, who came into the game trailing American League East-leading Boston by 3 1/2 games.
Minnesota rookie Kyle Gibson (1-2) surrendered four runs on four hits over six full frames in his third major league start.
Ryan Doumit had the only RBI for the Twins, who fell to 1-8 in July.
Celebrity Families of 2014 [PHOTOS]