Jung Ho Kang hit a three-run homer and Starling Marte and Gregory Polanco also went deep off Ian Kennedy in support of Burnett (5-1), who won his fifth straight start. Andrew McCutchen, Neil Walker and Francisco Cervelli each had three of the Pirates' 15 hits.
Pirates starters are 7-0 during the winning streak.
"The game's kind of funny," manager Clint Hurdle said. "We've had times here where the starters don't get any wins. It just depends on when you score runs, how it lines up. It's just one of those strange sequences of the game. It's nice to see that when the starters pitch well they do get a mark that falls in the right column."
Burnett deflected praise to the hitters.
"It's a nice little run the offense is on," Burnett said. "They came out swinging the bats tonight. They're playing hard all the way around. It's fun to be a part of."
The Pirates' first six runs scored on homers, including no-doubters by Kang and Polanco. Kang's shot with two outs in the first, his third, went an estimated 430 feet into the second deck in left field. Polanco led off the second with a 414-foot homer to center, his second.
Marte hit a two-run shot in the third, his 10th. McCutchen was aboard on a leadoff single.
Burnett allowed five runs, four earned, and eight hits in 5 2/3 innings, struck out six and walked two.
"He's had a very good start to the season," manager Clint Hurdle said. "We could have defended better to help him. Probably would have kept some of the stress off in the fourth and fifth."
After jumping to a 7-0 lead, the Pirates allowed two runs each in the fourth and fifth innings.
"The game's kind of funny," Hurdle said. "We've had times here where the starters don't get any wins. It just depends on when you score runs, how it lines up. It's just one of those strange sequences of the game. It's nice to see that when the starters pitch well they do get a mark that falls in the right column."
Kennedy (2-5) was chased by McCutchen's RBI double with two outs in the fourth. He lost his fourth straight start, allowing seven hits and seven runs, striking out five and walking two. Kennedy has allowed seven homers and 20 earned runs in his last four starts.
"It's really frustrating," Kennedy said. "Fastball command was all over the place. They hit a couple of breaking balls for homers. It's really, really frustrating, really inconsistent, not what I like to do. As a pitcher you try to go out there and be as consistent as possible. This has been a real test so far, the first month or so that I've pitched."
Padres: RHP Brandon Morrow, on the DL with right shoulder inflammation, threw 45 pitches in a simulated game. He'll throw again during the weekend and if all goes well, could be sent out for a rehab start.
Pirates: LHP Francisco Liriano (2-4, 3.86) is 1-2 with a 2.42 ERA in four career starts against San Diego.
Padres: Ace James Shields (6-0, 3.75) makes his first career start against the Pirates.