Norris suffered through a 12-game losing streak last year, and failed to get out of the first inning against the A's. But he was 4-1 in his five starts before that dating to last year.
"Bud helps me a lot every start," Peacock said. "Even between innings he goes over things and keeps me calmed down."
Peacock got himself out of a slight jam in the fourth inning of Tuesday's game and partly credited Norris.
"He told me when things get a little out of hand to take a walk around the mound until I'm ready to pitch again," Peacock said.
Houston manager Bo Porter said Peacock also learned something about holding runners after the A's stole a couple of easy bases.
"They did a good job of reading him," Porter said. "It's our job not to let that happen. We can't allow them to think we're robotic to the plate. We need to vary things."
Rick Eymer is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.