Wells delivered a three-run shot off Jonathan Sanchez (1-6) before the game's first out was recorded. After Jesus Montero singled, Smoak followed with a two-run blast for the Mariners.
Wells added a two-run triple in the fourth to knock out Sanchez, and finished with five RBI for Seattle in the opener of a four-game set.
Dustin Ackley added a solo homer while Ichiro Suzuki chipped in with two hits and an RBI for the Mariners.
Jason Vargas (9-7) collected the win, allowing three runs on seven hits in a six-inning effort.
Sanchez was roughed up for seven runs on seven hits, lasting only 1 1/3 frames for the Royals.
Billy Butler smacked a two-run homer and Salvador Perez added a solo shot for Kansas City.