Miami had lost eight of nine before its winning streak. The Marlins have swept consecutive three-game series on the road for the second time in team history.
Stanton's walk keyed a four-run eighth. The slugger saw eight pitches from Andrew Cashner (2-2) and all of them registered at least 101 mph.
Nolasco (4-0) allowed two runs and five hits in seven innings to tie Dontrelle Willis for the club record with his 68th career win.
In Washington, Cole Hamels pitched eight innings of one-run ball and Hunter Pence hit a pair of two-run homers to lead Philadelphia past Washington.
The Phillies batted around in the ninth, scoring six runs, and Hamels was lifted for pinch-hitter John Mayberry when his spot came up the second time in the inning.
Philadelphia snapped a seven-game losing streak against Washington dating to last year and avoided the sweep in the three-game series.
Washington rookie Bryce Harper stole home in the first inning, just the latest in an already growing list of accomplishments for the 19-year-old. But the Nationals lost a key player when right fielder Jayson Werth broke his left wrist while attempting a sliding catch.
In San Francisco, pinch-hitter Hector Sanchez singled over a five-man infield with the bases loaded in the 11th inning, giving San Francisco a victory over Milwaukee.
Buster Poster singled off sidearm submariner Tim Dillard (0-1) leading off the inning and pinch-runner Emmanuel Burriss moved to second on Angel Pagan's sacrifice bunt.
Travis Ishikawa's run-scoring double for the Brewers handed fill-in closer Santiago Casilla his first blown save in the ninth.
In Denver, Brandon Beachy pitched effectively into the seventh inning, Freddie Freeman hit a three-run homer and Atlanta beat Colorado for a three-game sweep.
Dan Uggla homered, singled and drove in two runs for the Braves, who are a major league-best 18-7 since April 10. The Rockies went 3-6 on their homestand.
Beachy (3-1) allowed two runs and four hits in 6 1-3 innings, retiring 14 straight during one stretch. Cristhian Martinez tossed 2 2-3 hitless innings for his first save.
In Houston, Tyler Greene hit a career-high two homers and drove in four runs, Adam Wainwright kept up his dominance of the Astros.
Allen Craig also homered as St. Louis stopped a three-game skid and ended Houston's five-game winning streak.
Wainwright (2-3) improved to 10-1 in 17 career appearances against the Astros - his most wins against any team.
J.A. Happ (2-2) allowed a season-high six runs in five innings.
In Chicago, David DeJesus drew a bases-loaded walk in the 11th inning to lift Chicago over Los Angeles.
Darwin Barney led off the 11th with a double. Wellington Castillo was intentionally walked and pinch-hitter Jeff Samardzija was hit by a pitch to load the bases. On a 3-2 pitch, DeJesus drew the game-winning walk.
Starlin Castro hit a two-run single for the Cubs, who overcame an early 3-0 deficit. They tied it on Tony Campana's double in the ninth off closer Javy Guerra. DeJesus, who would have been the winning run, was thrown out at home.
It was Guerra's third blown save in 11 chances. Rafael Dolis (2-2) got the win, while Jamey Wright (1-2) took the loss.
The start was delayed 2 hours, 41 minutes by rain. Dodgers center fielder Matt Kemp was a late scratch due to tightness in his left hamstring. He pinch-hit in the seventh and flied out.
In New York, R.A. Dickey baffled the Diamondbacks with his knuckleball, pitching shutout ball into the ninth inning to lead New York past Arizona.
Dickey (4-1) allowed four hits in eight-plus innings, struck out four and walked four, coming within three outs of his third career shutout. Frank Francisco earned his seventh save in eight chances.
Daniel Murphy hit a two-run single in the first and Josh Thole had an RBI single in the fifth. Mets shortstop Ruben Tejada left in the fifth after straining his right quadriceps.
In Pittsburgh, Mat Latos struck out a career-high 11 over six sharp innings in Cincinnati's victory over Pittsburgh.
Drew Stubbs had three hits, including a two-run homer, and scored three times. Todd Frazier added his first home run of the season.
Latos (2-2) escaped a bases-loaded jam in the first and then cruised. Pittsburgh never got a runner past second base over his final five innings. The right-hander gave up two hits while walking three.
Three relievers upped Cincinnati's strikeout total to 17, tying a club record for a nine-inning game.
Charlie Morton (1-3) gave up five runs, four earned, and seven hits in six innings.
