Burnett (1-2) lost his bid with two outs in the seventh on Carlos Beltran's double to right-centre. That was the lone hit given up by the 36-year-old right-hander in seven dominant innings.
Burnett struck out eight. He got the 2,000th strikeout of his 15-year career when he caught Beltran looking in the second.
Mark Melancon, Tony Watson and Jason Grilli completed the one-hitter.
Burnett's no-hitter came on May 12, 2001, for the Florida Marlins in San Diego. That game was also notable for his nine walks. Burnett walked none against St. Louis.
Cardinals rookie Shelby Miller (2-1) pitched well despite taking his first loss in four career decisions.
PADRES 7, DODGERS 2
LOS ANGELES (AP) — Clayton Kershaw gave up his first three home runs of the season in a span of three innings and the San Diego Padres beat the Los Angeles Dodgers to finish a three-game sweep.
Everth Cabrera, Chris Denorfia and Kyle Blanks all connected off Kershaw (2-2), who entered with a 1.16 ERA in three starts. But the 2011 NL Cy Young Award winner left this one trailing 5-1 after throwing 109 pitches in 5 1-3 innings.
Boosted by the return of slugger Chase Headley from a broken thumb, the Padres pounded out 13 hits and beat one of baseball's best pitchers. After arriving with a 2-10 record, San Diego earned its first sweep at Dodger Stadium of three or more games since July 2006.
It was the first series between the NL West rivals since their wild brawl last week in San Diego.
Cabrera had three hits and scored twice as the Padres sent Los Angeles to its fourth straight defeat. Headley was back at third base and went 1 for 4 with a late RBI single.
Brad Brach (1-0) retired Skip Schumaker on a comebacker with the bases loaded in the fifth.
NATIONALS 6, MARLINS 1
MIAMI (AP) — Ross Detwiler departed with a lead for the third start in a row and this time the bullpen held on as Bryce Harper and the Washington Nationals beat the Miami Marlins.
Harper, back in the Nationals' lineup after missing one game with the flu, hiked his average to .364 with four hits and improved to 9 for 20 against Ricky Nolasco (0-2). Harper hit two solo homers off Nolasco on opening day.
Detwiler (1-0) allowed one run in seven innings, which increased his ERA to 0.90. He left his first two starts with the Nationals ahead 5-1 and 4-1, but both times received no decision.
ROYALS 1, BRAVES 0
ATLANTA (AP) — Wade Davis pitched seven sharp innings, Jeff Francoeur had an RBI single and the Kansas City Royals stopped Atlanta's 10-game winning streak.
The Braves were seeking their first 13-1 start since 1994. But the Atlanta hitters — who homered five times off the Royals on Tuesday — were shut down.
Davis (2-0) gave up five hits, didn't walk anyone and struck out seven. Greg Holland worked a scoreless ninth for his third save.
Mike Minor (2-1) allowed five hits, including Francoeur's single in the fourth, and in six innings. The left-hander's ERA over three starts is 0.95.
BREWERS 4, GIANTS 3
MILWAUKEE (AP) — Pinch-hitter Blake Lalli lifted a long single in the bottom of the ninth inning that sent the Milwaukee Brewers over the San Francisco Giants.
With the score tied, one out and the outfielders playing in, Lalli stepped to the plate for just the sixth time this season.
Lalli lofted a deep fly ball well over the head of left fielder Gregor Blanco for his first hit of 2013. Milwaukee extended its longest winning streak this year to three.
Brewers starter Kyle Lohse did not allow a hit through the first five innings as Milwaukee built a 3-0 lead.
Jim Henderson (2-0) pitched the ninth. Santiago Casilla (1-1) took the loss.
REDS 1, PHILLIES 0
REDS 11, PHILLIES 2
CINCINNATI (AP) — Jay Bruce hit a pair of bases-loaded singles that sent the Cincinnati Reds to a couple of wins over Philadelphia.
First, the Reds finished their game suspended overnight by rain. Several hundred fans were in the stands to see Phillippe Aumont (1-2) pick the game up in the bottom of the ninth and give up Bruce's bases-loaded single only four batters later.
Aroldis Chapman (2-0) got the win without even warming up on Wednesday — he'd retired the last three batters before the rain came the previous night.
Then, the Reds completed their first series sweep of the Phillies since 1996.
Bruce hit a bases-loaded single that highlighted a five-run rally in the second inning off left-hander John Lannan (0-1).
Reds starter Mike Leake (1-2) drove in a run with his first career triple during the big inning.