Cousins was jarred in the second inning when Red Sox catcher Jason Varitek's foul ball hit him. The umpire worked another 1 1/2 innings, but he did not come back out for the top of the fourth.
Cousins, who has 29 years of Major League experience, was diagnosed with a bruised clavicle. He is questionable for tonight's ALCS Game 7 at Tropicana Field.
"He said his collarbone was hurting him, but he said he was all right," Varitek said after the Red Sox defeated the Rays, 4-2. "I asked him when I came back out there, and then I didn't know what happened after that."
Crew chief Tim McClelland, working first base in the game, called his umpires to the infield to discuss how to proceed, before deciding to change his uniform and don the home-plate umpiring gear for the remainder of the contest.
Varitek said that the umpiring change did not affect the complexion of the game.
"I think that they maintained consistent zones," Varitek said. "Derryl had a consistent zone, and Tim always has a consistent zone. He's one of the best in the game, period."
During the delay, Rays starter James Shields returned to the bench with the rest of his team, as the Red Sox waited to bat in the top of the fourth, with Boston leading, 2-1, at the time.
Shields said the umpiring change did not affect him, saying McClelland "came in and did a great job." Hitters, like Tampa Bay's Carl Crawford and Boston's Dustin Pedroia, also said the in-game change -- while different than usual -- did not impact the outcome of the contest.
Said Rays catcher Dioner Navarro: "They've still got to throw the ball over the plate. It was no different. Stuff happens and unfortunately guys have to get out of the game, and Tim came in. Nothing really changed; they did a great job. Shields had enough time to come back and warm up, and I don't think none of that delay had to do with anything [with the game]."
Red Sox manager Terry Francona had left-hander Javier Lopez warming up before Beckett went to the mound for the bottom of the fourth, and Francona said the maneuver played slightly into the lengthy top half.
"The reason we did that, Josh didn't complain or anything like that, but it was a long delay," Francona said, "and if he goes out and struggles, when we rush Javi, that doesn't do any good.
"So we wanted to give [Lopez] time to warm up, throw some pitches so he didn't get rushed into a game. But it was just almost like a rain delay. It was a short one, but it was kind of an oddity we just wanted to be prepared for."
With McClelland moving behind the plate, Sam Holbrook went to first base, Brian O'Nora shifted to second, Brian Gorman to third and Alfonso Marquez remained in right field.
According to Mike Port, Major League Baseball's vice president for umpiring, who was on site for Saturday's game, the decision to have McClelland replace Cousins behind the plate was made because McClelland is the crew chief, was umpiring at first and due to rotate from first to home plate for Game 7 on Sunday.
No decision is expected until today on whom will umpire behind the plate for Game 7.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.