Despite the result, it was a solemn Kansas City clubhouse. Gordon was carted from the field in the fourth inning with a left groin injury and then sent for a MRI exam.
Gordon told the medical staff he heard something pop. He ran into the wall in pursuit of second baseman Logan Forsythe's fly, which turned into an inside-the-park homer as Gordon lay on the warning track.
"Doctors didn't feel like it was detached from the bone, which is a good thing," Royals manager Ned Yost said. "We'll just have to see."
Yost is not optimistic Gordon will return anytime soon, acknowledging it might be months.
Winning pitcher Jeremy Guthrie said he hopes to have Gordon back in the "next month or two."
Rays right-hander Chris Archer (9-6), who was a candidate to start the All-Star Game, had the worst outing of his career, giving up a career-high nine runs and 12 hits in six innings. Archer entered the game 6-0 with a 0.77 ERA in seven road starts this season. He had allowed three or fewer earned runs in a club-record 20 consecutive road starts.
"It's just disappointing in the fact I didn't hardly give my team a chance to win," Archer said. "We put up seven runs, and when we usually do that, we win. Obviously, I hold myself to a higher standard. I want to give the team a better performance."
The Royals, however, tattooed him. Center fielder Cain drove in three runs, hitting a two-run homer in the fourth over the center field wall.
Dyson, who replaced Gordon, homered, his first since June 25, 2014, another inside-the-park job. When Rays left fielder David DeJesus dived but failed to catch Dyson's low liner in the sixth, the ball rolled to the warning track as the speedster circled the bases.
Gordon, not the homer, was on Dyson's mind after the game.
"That's a devastating moment for the team and the organization," Dyson said of Gordon's injury.
Escobar finished with four singles, his fifth career four-hit game and first this season. Two Escobar hits caromed off Archer's body in the first and fifth innings.
The Rays (43-44) lost for the 10th time in 11 games and fell below .500.
Guthrie (7-5) picked up the victory after a shaky first inning in which he walked three and threw 30 pitches. Guthrie went six-plus innings, allowing four runs, three earned, on eight hits and four walks.
Rays catcher Rene Rivera clubbed three hits, including a home run the ninth off Joe Blanton, who failed to finish the inning and was charged with three runs.
Greg Holland was summoned to get the final two outs and pick up his 17th save in 19 opportunities, but not before giving up a two-run single to third baseman Evan Longoria. Holland struck out pinch hitter Grady Sizemore to end the game with Rays on second and third base.
Archer, who gave up only four earned runs in 46 2/3 innings during seven previous road starts, yielded seven runs in the first five innings Wednesday.
Cain, who sat out the previous two games with a tender hamstring, homered in the third with Escobar aboard. Cain's infield single in a five-run fifth scored third baseman Cheslor Cuthbert.
The Royals batted around in the big fifth, which also included a two-run double by designated hitter Kendrys Morales. First baseman Eric Hosmer and catcher Salvador Perez delivered run-producing singles in the inning. All the runs scored with two outs, and Kansas City took a 7-3 lead.
"It is becoming kind of like a broken record," Rays manager Kevin Cash said. "We keep talking that we're in a rut. We know it. We can't quite find that break to get us out of it.
"It shows a lot about the club. We get Holland into the game and put pressure on them where we have the lead-taking run at the plate and the tying run at second base. It's little bit of a frustrating day."
NOTES: The Rays designated LHP Everett Teaford for assignment and reinstated RHP Andrew Bellatti from the disabled list. ... The Royals optioned LHP Brandon Finnegan, who picked up the win in the second game of the doubleheader Tuesday, to Triple-A Omaha. RHP Aaron Brooks, who was the 26th man for the doubleheader, remained on the roster. ... Royals LHP Jason Vargas threw 60 pitches in a simulated game Wednesday. He will make a rehab start Monday for Double-A Northwest Arkansas. ... Rays rookie RHP Nathan Karns and Royals RHP Yordano Ventura, who will come off the DL, will start the Thursday series finale.