Washington allowed Nelson Cruz to swing away in the third inning, and the left fielder crushed 438-foot solo home run to straightaway center field.
Two innings later, Vladimir Guerrero got a 3-and-0 fastball from Rays left-hander David Price and drilled a run-scoring double to center as the Rangers opened the best-of-five series with their first postseason win since 1996.
"They gave me the green light, you know, so I was looking for a pitch right down the middle, and that's what I got," said Cruz, who hit 22 home runs during the regular season.
He said getting to unwind on a 3-and-0 count is nothing new.
"I have been doing that my whole career, even in the Minors," he said, "so I am used to it. I look for a pitch right down the middle, and if I get it, I swing. If I don't get it, I take it."
He got one grooved and, "I hit it pretty well," he said.
The two-out home run gave Texas a three-run lead and Guerrero's run-producing double in the fifth bumped the Rangers' lead to five runs.
"I thought [Price] looked pretty typical in the sense that the velocity was there, mixed in with his curveball," Rays manager Joe Maddon said. "A couple of big 3-and-0 hits against him, the home run by Cruz and then the double by Vladdy, kind of built that picket fence.
"They went two, one, one, one and that kind of hurt."
Jim Street is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.