Presley reached four times and scored twice as Pittsburgh snapped a five-game losing streak. Josh Harrison doubled, singled and scored twice.
"It was a good team win," manager Clint Hurdle said. "We had some guys throw some things in from top to bottom today."
Burres (1-0), who was promoted from Triple-A Indianapolis on Thursday, allowed one run and five hits over 5 1/3 innings. The left-hander started on short notice after Jeff Karstens was scratched with what the team is calling "fatigue."
"(Burres) did a very professional job," Hurdle said. "He's pitched in the big leagues before so he wasn't overwhelmed with anything. I thought he kept the ball down especially well today."
It's been a rough season for Burres, who went 4-5 with a 4.99 ERA in 20 games, 13 starts, for Pittsburgh last year. He had a 5-9 record and a 4.66 ERA with Indianapolis when he was promoted.
"I was anxious for Brian's start," Hurdle said. "To go down as he did, as professional as he did, start after start. Never a complaint. Hard work. Gets the opportunity and comes up here and pitches. To end up five-plus (innings) with one run on the day, that's just good stuff."
The 30-year-old Burres said it was nice to get a win in his return to the majors.
"I've been feeling good the last couple of weeks and it's good to just carry that feeling into my start today," he said.
"Most of the day I just tried to throw strikes and let my defense do the work."
Four Pirates relievers combined for 3 2/3 perfect innings, with Joel Hanrahan picking up his 33rd save in 36 chances. Jason Grilli got the last two outs of the sixth, Chris Leroux pitched the seventh and Jose Veras worked the eighth before Hanrahan struck out two in the ninth.
Carlos Pena went deep for the Cubs, who have lost nine of 12. The first baseman now has at least 25 homers in five straight seasons and six times overall in his career.
"I said this before, just the fact that I've been able to hit one in the big leagues is a blessing to me and I'm very grateful for it, let alone hit so many," Pena said.
Ryan Dempster (10-11) worked out of a couple of early jams and held Pittsburgh to three runs and seven hits over 6 1/3 innings. He struck out nine, two shy of his season best, and threw a season-high 121 pitches.
"I tried to survive those first couple innings, they fouled off a lot of pitches," Dempster said. "I was able to get out there and get into the seventh."
Pena connected in the second, hitting a drive to the deepest part of center field to give the Cubs the lead.
"That pitch I just left up a little bit and he did a good job of hitting it hard," Burres said.
Pittsburgh responded with two in the third. Presley led off with a triple off the right-field wall and Harrison followed with a single to right. Garrett Jones added a two-out RBI double.
"You just try to see pitches and get on base," Presley said. "I was familiar with Dempster from the last time facing him so I tried to be a little more aggressive."
Neither team mounted much offense after that. The Cubs stranded two runners in the third and fourth. The Pirates didn't threaten again until Presley's one-out triple in the seventh chased Dempster. Presley scored on Jose Tabata's two-out single off Kerry Wood.
Presley became the first Pirate to record two triples in a game since Andrew McCutchen on June 8, 2009. He has five triples on the season.
"Presley ignited us at the top, stayed on base and made some things happen," Hurdle said. "Harrison gave us some life."
The only damper on the day for the Pirates came when McCutchen was hit in the left hand in the first inning. He remained in the game to run the bases, but was replaced by Tabata before the Cubs batted in the bottom half.
The team said McCutchen does not have a fracture and is listed as day to day.
The Cubs promoted 1B Bryan LaHair from Triple-A Iowa. LaHair's 38 home runs for Iowa were leading the minor leagues. ... The Cubs announced that RHP Carlos Zambrano will not pitch for them again this season, even though his time on the disqualified list expires on Sept. 11. ... Pirates 1B Derrek Lee (left wrist) took batting practice and the team hopes to activate him from the 15-day disabled list on Sunday if all goes well. ... The Cubs will send RHP Casey Coleman to the hill on Saturday to face Pittsburgh RHP Ross Ohlendorf. Coleman has an 11.34 ERA in 19 2/3 innings at Wrigley Field this season.