The Rays snapped a three-game skid while keeping the Royals from winning a third straight game. Colby Rasmus finished off a 16-hit attack with his sixth career grand slam, which came on an 0-1 pitch from Peter Moylan to cap a five-run eighth.
Logan Morrison added to Tampa Bay's lead in the third with a two-run homer off Jason Hammel that pushed the Rays' lead to 3-0. Rickie Weeks Jr. followed with a solo shot to complete the back-to-back homers act, the third time the Rays have accomplished that this season.
"Offensively, a bunch of guys impacted the game today," Cash said. "LoMo, Colby Rasmus, Rickie Weeks. It's good to see Rickie get going. He's having some good at-bats."
The Rays' offense got busy again in the fourth. Corey Dickerson tripled home a run and scored on Brad Miller's sacrifice fly to make it 6-0.
Meanwhile, Archer dominated the Royals' offense, which had scored 14 runs in its previous two games, by posting eight scoreless innings and allowing just five hits while striking out 11 en route to his third win of the season.
Jorge Soler accounted for the Royals' run with an RBI double -- his first hit since being acquired by Kansas City -- off Jumbo Diaz in the ninth.
"These games are actually easier to take than losing games 1-0 or 3-2, when you can look at opportunities you had to maybe score a run that may have tied the game or scored a run and you didn't that could've ended up giving you the lead," Royals manager Ned Yost said. "These games happen."
MOMENTS THAT MATTERED LoMo's blast: Morrison has been hot, and that continued on Wednesday night when he connected for a two-run blast, giving the slugger a team-leading nine homers for the season while putting the Rays up 3-0. Morrison's barreled ball traveled 444 feet, tying his longest in the Statcast™ era (Sept. 2, 2016, was the other), and had a 107.4-mph exit velocity with a 27-degree launch angle. He has three home runs in his last five games.
Hammer time: Hammel wasn't at his best judging from what the Rays' bats were telling him on Wednesday night, but the veteran right-hander took one for the team. After using seven pitchers in Tuesday night's 12-inning win over the Rays, the Royals needed Hammel to go deep into the game, and he did just that. He might have allowed seven runs (six earned) on 13 hits, but he sucked it up to give his team seven innings.
WHAT ARE WORDS FOR? Royals catcher Salvador Perez, who was celebrating his 27th birthday on Wednesday, exchanged words with Archer after getting hit by a 96-mph fastball by the right-hander in the seventh. Players from both teams gathered on the top steps of the dugout as the two continued to have words until Perez was replaced with a pinch-runner at first base. More >
WHAT'S NEXT Royals: Left-hander Jason Vargas (4-1, 1.19 ERA) will get the ball for the series finale at Tropicana Field on Thursday at 12:10 p.m. CT. Vargas has been stellar since returning from Tommy John surgery in September, holding opponents to a .209 average.
Rays: Right-hander Jake Odorizzi (2-1, 2.88) will make his sixth start of the season when he faces the Royals in the finale on Thursday at 1:10 p.m. ET. Odorizzi has pitched well in his two starts since returning from the disabled list. On Saturday against Toronto, he retired 10 of the last 11 batters he faced en route to his second win of the season.