The Astros, meanwhile, eliminated left-hander Ryan Rowland-Smith from the competition for their fifth starting spot.
Morton, coming off a 2-12 season, gave up four singles and struck out five in dropping his spring ERA to 1.29. Pirates manager Clint Hurdle called it "our best outing of the spring."
Hurdle wasn't around to see Morton post a 7.57 ERA last season, but he has seen something quite different this spring.
"Just the overall demeanor of the man has looked very good and clean to me," Hurdle said. "So I don't have anything else to compare it to, but he definitely was very aggressive today."
Ronny Cedeno hit a two-run home run off Rowland-Smith in the first inning, but the Astros had decided before the game to send Rowland-Smith to the bullpen.
That leaves rookie Jordan Lyles, Nelson Figueroa, Lance Pendleton and Aneury Rodriguez in nominal competition for the fifth spot, although Pendleton has yet to pitch beyond two innings.
"There's times I don't make good pitches when I need to, but that's spring training. It's always been that way for me," said Rowland-Smith, who pitched two innings in his final start. "I just want to have a good week and a half and embrace whatever role they give me and contribute."
Lyles followed Rowland-Smith with 3 2/3 innings, giving up one run and striking out four.
Lyles had the best hit of the day off Morton, driving a ball into the left-field corner in the fifth inning. But he pulled up after reaching first base, thinking the ball had gone out when first-base coach Cesar Cedeno said, "Good job."
Astros left-hander Wandy Rodriguez, who missed his last start due to tendinitis in his shoulder, threw lightly Sunday morning and is scheduled to make his next start Tuesday. ... Pirates OF Garrett Jones took some treatment for minor neck stiffness Sunday. ... The Astros' Koby Clemens had to leave the game after fouling a pitch off his knee in the ninth inning. ... Steve Pearce, who had two hits for the Pirates, in eight for his last 15.