KANSAS CITY, Mo. — As the zeroes piled up and a historic drought dragged on, as a baseball season teetered on the brink, Kauffman Stadium turned quiet Monday night.

There had been sounds, of course. A cascade of boos after another woeful start from Ian Kennedy. An overenthusiastic cheer when Lorenzo Cain reached third base following a one-out double in the fourth inning. But then, there was mostly silence, the kind of muted indifference that accompanies the worst stretch of offense in franchise history.

In a 12-0 loss to the Tampa Bay Rays, the Royals extended their franchise record scoreless drought to 43 innings. On a Monday night in Kansas City the stadium cleared out early, the losing streak hit five games, and a dream of a third postseason appearance in four seasons felt like folly.

The Royals became the 10th team in history — and the first in 25 years — to be shut out in four consecutive games. The last team to experience this kind of humiliation was the 1992 Chicago Cubs.

Five days earlier, the Royals had dressed in a joyous clubhouse, laughing and celebrating in the wake of a 6-4 victory over the Colorado Rockies. Eric Hosmer had offered a mammoth walk-off shot in the bottom of the ninth, and in the moments after the first walk-off homer of his career, Hosmer called his blast a swing “that can really get things going for the team.” In the five days since, his team had lost five consecutive games and been outscored 35-2, including a 35-0 run that began in the third inning on Thursday afternoon.

The stretch has included a three-game sweep at Progressive Field in Cleveland. The contrast between a walk-off victory and a record scoreless streak has only served to accentuate the vagaries of baseball and the limits of this team.

On Monday, the Royals dropped to 64-66, two games under .500 for the first time since July 18. Starting pitcher Kennedy was bludgeoned for seven runs in 2 2/3 innings, his ERA in August soaring to 9.57. The Royals managed just one hit off Tampa Bay starter Austin Pruitt, who tossed six innings after surrendering 14 earned runs in his last three starts.

For a second straight day, a game turned into a rout in the early innings. On Sunday, the Royals were battered for 12 runs in the first two innings in a loss to the Indians. On Monday, Kennedy allowed a three-run homer to Lucas Duda, formerly of the New York Mets, and a two-run shot to Wilson Ramos. In all, the Rays piled up six extra-base hits, turning Kennedy into a pitching machine.

By the top of the ninth, the Rays had piled on with another four runs against reliever Kevin McCarthy. First baseman Logan Morrison, who spent much of his childhood in the Kansas City area, roped a three-run homer to right field.

By the bottom half of the ninth, the only drama surrounded the scoreless drought. Some day, the Royals will score a run again. But it would not happen on Monday night.