Peacock gave up a leadoff single to Dustin Pedroia before retiring Jackie Bradley Jr., Mookie Betts and Hanley Ramirez in order.
With two outs in the second, he had some traffic on the bases, but limited the damage to one run.
After getting Pablo Sandoval to ground out and striking out Sam Travis, Peacock gave up consecutive singles to Allen Craig, Sandy Leon and Deven Marrero for a run before getting Pedroia to line out.
Peacock retired the side in order in the third, giving way to right-hander Francis Martes for the fourth.
"It's the best I've felt all spring," Peacock said. "Offspeed is still coming along. It's still not as sharp as I want it to be. But still working on it."
Out of Minor League options, Peacock knows he will have to string together more of these kinds of outings if he hopes to win a spot on the Astros' Opening Day roster. In seven appearances, three starts, spanning 12 1/3 innings this spring, he has allowed eight runs on 15 hits, with three home runs, four walks and six strikeouts.
"I don't know," he said of the Astros' roster status. "I know with my situation and where I stand. I don't know what's going to happen but I hope to stay here. I'm just trying to pitch well to have a chance."
Manager A.J. Hinch, who was in West Palm Beach with the other split squad, has indicated he would like to open the season with 13 pitchers. Whether or not that helps Peacock's case remains to be seen.
"Well, there's a lot of guys, a lot of good pitchers here," he said. "So, I'm just trying to battle and just see what happens."
Peacock finds himself out of options for the first time, a status which can be good or bad. It can force a team to keep a player on the big league roster for fear of losing him, or a team may decide to part ways with the player. Peacock is unsure how his status affects him.
"I have no idea," he said. "This is my first [time]. ... I don't know what's going to happen. But just trying to pitch my way, hopefully make this team."
Bullpen or rotation, he has no preference.
"I just want to pitch in the Major Leagues, whatever way I can and just trying to do well," he said.
This and that
• Martes was impressive, tossing three perfect innings with three strikeouts. It was his fourth Grapefruit League appearance and first scoreless outing of the spring.
• Evan Gattis went 2-for-4 with a double, a run scored and an RBI.
• Reid Brignac went 2-for-2 with a double and two RBIs.