Three of Correia's last four appearances had come out of the bull pen, but he was given the start Wednesday when Jeff Karstens was unable to take his turn due to a hip injury.
Correia (10-8) allowed the Astros one run and was lifted after throwing only 67 pitches.
The Pirates won their second in a row to climb with a game of the second wild card spot in the National League. Houston moved within five losses of reaching 100 for the season.
Pittsburgh built a 5-1 lead through four innings and moved in front for good on RBI singles from Garrett Jones and Gaby Sanchez in the first.
Brock Holt drove in two Pittsburgh runs with an infield single in the second and a sacrifice fly in the fourth.
The last two Houston runs came on a two-out, ninth-inning homer by Brandon Laird off Jason Grilli. It was the first career homer for Laird, who was obtained by Houston this week off waivers from the New York Yankees and was playing in his 13th major league game.
The loss went to Fernando Abad (0-3), who gave up four runs on six hits in four innings.