With the score tied at 2, Brian McCann led off the eighth with a single off Ryan Madson (2-4). Pinch-runner Jair Jurrjens moved to second on Yunel Escobar's sacrifice. Diaz followed with his run-scoring double to the center-field wall.
Pinch-hitter Garret Anderson added his first career pinch-hit homer, a two-run shot off Madson.
Rafael Soriano pitched the ninth for his eighth save.
Philadelphia has lost 12 of 15 and is only two games over .500 and two games ahead of the fourth-place Braves.
Philadelphia left-hander J.A. Happ, coming off his first career shutout in a 10-0 win at Toronto on Saturday, gave up a two-run homer to Casey Kotchman in the fourth inning before retiring the next seven batters. He gave up seven hits and two runs in seven innings.
The Phillies pulled even with two runs off Javier Vazquez in the sixth.
The Braves, who were 0-9 against the Phillies at Turner Field last season, completed their first home sweep of Philadelphia since April, 2005.
The Phillies had a chance to take the lead in the eighth when Jayson Werth walked, stole second and advanced to third on McCann's throwing error. Werth tried to score on Mike Gonzalez's wild pitch to the screen. McCann recovered quickly and threw back to Gonzalez (3-0), who made the tag on Werth's headfirst slide.
Vazquez shut out the Phillies for five innings before giving up two runs in the sixth.
Vazquez gave up seven hits and two runs in 5 1-3 innings. He did not walk a batter and struck out five.
Greg Dobbs' double over Gregor Blanco in center field drove in Chase Utley, who led off with a single. Reliever Peter Moylan gave up a tying groundout to Pedro Feliz to drive in Werth.
Diaz, making his second straight start in left field, led off the fourth with a single and scored on Kotchman's two-run homer. It was only Kotchman's third homer and his first since May 8 against the Phillies' Brad Lidge.
Jimmy Rollins grounded out in his first at-bat before ending a career-worst 0-for-28 slump with a single to right field in the third inning. It was his first hit since June 18. He added a fifth-inning single.
NOTES: RHP Tim Hudson proclaimed he cleared his "last hurdle" after throwing 90 pitches in the bullpen before the game. Hudson, who had elbow ligament-replacement surgery on July 27, 2008, is scheduled for his first rehab assignment on July 19 at Class A Myrtle Beach. ... Phillies OF Raul Ibanez (groin) had his first rehab game at Double-A Redding pushed back to Thursday or Friday. ... Happ's fifth-inning single past 2B Martin Prado was his first major league hit. ... CF Nate McLouth missed his fifth straight start with a strained left hamstring.
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