Dyson has made just four appearances in the first 17 days of July. He had nine through the first 17 days of June and 14 for the month.
"Rest," Dyson said. "Everybody needs rest, so it's pretty important. I felt fine."
Dyson was second in the American League in appearances in the first half, with 44.
"I didn't even know that," Dyson said.
Manager Jeff Banister said the Rangers were eager to get Dyson time off, although they would have preferred not to lose 11 of 14 to accomplish it.
"We need for him to do what he did before the time down," Banister said. "We know what Sam is capable of doing when he gets consistent appearances. We'd like to keep it that way, but it doesn't always work that way."
Dyson doesn't want too much time off.
"I've taken time off before and not been very good," Dyson said. "Today, I had the luck of the draw. I threw strikes, that was the main thing."
T.R. Sullivan has covered the Rangers since 1989, and for MLB.com since 2006. Follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.