The Astros' victories on Friday and Saturday gave them their third series victory in their last five series. They still haven't won three games in a row since winning four in a row from May 21-25.
The loss assures the Astros the No. 1 pick in the 2013 First-Year Player Draft. They also selected first in this year's draft.
Burnett struck out 11 and walked one in picking up his 16th win of the season.
"He was in complete control from start to finish," Pirates manager Clint Hurdle said.
Moore was the only player to manage hits off Burnett in the first seven innings, recording a single, a double and his ninth homer of the season, a solo shot to right field in the sixth.
After a 3-for-4 performance against Burnett, Moore is 6-for-12 in his career against Burnett with two homers. He said he tried to lay off the curveball down in the zone and focused on getting a fastball over the middle of the plate.
Moore didn't discuss his game plan with his teammates, but he isn't sure that would've helped.
"That's how he pitches," Moore said. "He comes right after you. Even if you have a good game plan, sometimes he's tough to hit because he's got good stuff."
Astros starter Jordan Lyles matched Burnett with four scoreless innings to start the game. The game turned in the fifth inning after Lyles allowed two singles to open the inning. A 3-2 fastball to the next batter, Most Valuable Player candidate Andrew McCutchen, was called a ball, loading the bases.
"It looked on the replay that maybe McCutchen thought I had him," Lyles said "I think he might've been walking back to the dugout."
"I thought the 3-2 pitch to McCutchen was pretty good," DeFrancesco said.
That ended up being Lyles' final pitch. DeFrancesco decided to bring in left-handed reliever Wesley Wright to face the left-handed hitting Garrett Jones, but Pirates manager Clint Hurdle pinch-hit with Gaby Sanchez, a righty. Wright hit Sanchez with a pitch to give the Pirates their first run.
Wright struck out Pedro Alvarez before making way for reliever Mickey Storey. Jose Tabata's walk on four pitches brought home a run. Two bloop singles over shortstop Tyler Greene plated two more runs. Storey struck out A.J. Burnett and got Alex Presley to ground out to end the four-run inning.
Lyles' ERA in the fifth inning this season is 17.22 (19 1/3 innings). DeFrancesco said Lyles' previous struggles toward the end of his starts was a factor in the decision to bring in Wright.
"Just the way it was starting to shape up, I had that in the back of my mind," DeFrancesco said. "When I saw three lefties coming up, we had Wesley Wright, who had been throwing the ball well for us, and unfortunately we hit the guy. A couple of bloop hits and that walk got them going."
Lyles threw 78 pitches, his lowest pitch count of the season.
"It is what it is," Lyles said of being pulled. "Not really sure. It's whatever."
The Pirates scored three more in the seventh off reliever Enerio Del Rosario behind three RBI singles by Alvarez, Tabata and Burnett.
And while the Pirates kept on adding runs, Burnett kept mowing down Astros hitters. Third baseman Brandon Laird was the only Astro other than Moore to record a hit on Sunday.
"Overall, A.J. just shut us down pretty much the whole game and towards the end of the game our relief pitching couldn't shut them down," DeFrancesco said.
Second baseman Jose Altuve tweaked his groin while running the bases in the third inning and exited for pinch-hitter Jimmy Paredes in the sixth. Taking Altuve out of the game was precautionary, DeFrancesco said.
"He said he was fine, just tightness, but we're probably going to give him a day off tomorrow," DeFrancesco said.
This was the final meeting between the Astros and Pirates with both teams in the National League Central. The Astros will be moving to the American League West in 2013.