Bourn had three hits, scored twice and stole a base hours after learning he'll head to the Midsummer Classic to replace injured Washington infielder Ian Desmond.
"It's always an honor to be with those kind of players," Bourn said. "There's only a certain amount going. I'm just happy to sneak in there and I hope I can help the NL win the game."
The five-time defending NL East champion Phillies are freefalling since Chase Utley returned to the lineup, losing nine of 10. They just got Ryan Howard back on Friday night and have lost two in a row, though the former NL MVP didn't play in this loss.
"It's hard for us to win because we just don't play good enough," manager Charlie Manuel said.
Hanson (10-5) allowed three runs and six hits, striking out six in seven-plus innings. Eric O'Flaherty worked the rest of the eighth and Craig Kimbrel finished for his 24th save in 25 tries.
"I feel really good where I'm at right now," Hanson said.
Things are so bad for the last-place Phillies that even when they do something right, it looks ugly. Hunter Pence ran over third-base coach Juan Samuel on his way to scoring a run in the second inning.
In the seventh, All-Star closer Jonathan Papelbon made his biggest save of the season. Papelbon leaped from his seat and stopped a fan from climbing into Philadelphia's bullpen.
Phillies starter Joe Blanton (7-8) allowed six runs -- five earned -- and nine hits in 6 1-3 innings.
The start was delayed 58 minutes because of dark skies, lightning and threat of a thunderstorm.
McCann, who hit a grand slam in Friday's 5-0 win, crushed a 2-1 pitch way out to right to put the Braves up 1-0 in the second. It was the 20th homer allowed by Blanton, and that's most in the NL.
"It's a great yard to hit. I enjoy coming here," McCann said.
After the Phillies took a 3-1 lead in the second, Martin Prado's RBI double with two outs in the third cut it to 3-2. The Braves went ahead with two more runs in the fourth.
Freddie Freeman and Chipper Jones started with consecutive singles. McCann lined an RBI single to right to tie it at 3. A fielding error on Pence allowed Jones to advance to third on the hit. He scored the go-ahead run on Andrelton Simmons' sacrifice fly to right.
The Phillies scored three in the second, an offensive outburst for a team has 15 total runs in its last seven losses.
With two on and one out, Juan Pierre ripped a double to right. Pence took a wide turn around third, barreled into Samuel and kept going. A three-time All-Star during his playing career, Samuel ended up flat on his back and his helmet flew off. Players in both dugouts laughed, though the affable Samuel didn't seem too happy with himself.
After John Mayberry Jr. was intentionally walked to load the bases, Blanton lined an RBI single to right to give the Phillies a 2-1 lead. Another run scored on Jimmy Rollins' fielder's choice grounder.
Simmons, the 22-year-old shortstop, made two outstanding defensive plays to help Hanson. Simmons robbed Placido Polanco of an infield hit by charging hard on a slow roller and making a quick throw to first. He later robbed Utley of a hit with a diving grab on a hard grounder up the middle. Hanson simply turned around and shook his head in admiration.
Prado's RBI single in the seventh put the Braves up 5-3. Bourn then stole a run to make it 6-3. Bourn ran home when Jason Heyward struck out and the ball got away. He charged toward the plate on catcher Carlos Ruiz's throw to first and originally was credited with a steal of home, but the play was changed to a fielder's choice after the game.
NOTES: Roy Halladay threw his third bullpen session before the game and could start a rehab assignment after the All-Star break. The two-time Cy Young Award winner may rejoin Philadelphia's rotation by mid-July. He's been sidelined since May by a lat strain. ... Blanton has allowed a homer in 11 straight starts after giving up just one in his first seven starts. ... Jones extended his hitting streak to 13 games. ... The Braves are 9-3 in last 12 road games and 25-17 overall, which is the best record in the NL. ... Atlanta 2B Dan Uggla, voted to start the All-Star game, is 9 for 92 and hitless in his last 19 at-bats, dropping his average to .220. ... The Phillies had their 263rd straight sellout, including postseason. ... Jair Jurrjens (2-2, 5.19) pitches for the Braves against Vance Worley (4-5, 3.46) in Sunday's series finale.