The Braves, who have won three of four and lead second-place Washington by 5½ games in the NL East, retired former All-Star third baseman Chipper Jones’ number before the game.
Teheran (6-4) allowed four hits, one walk and struck out 10.
The NL West-leading Diamondbacks have lost three of four. They were shut out for the first time since losing 5-0 at San Francisco on Sept. 26, a span of 85 games.
Atlanta closer Craig Kimbrel earned his 23rd save in 26 chances. After Aaron Hill grounded out, Kimbrel walked Paul Goldschmidt and then Miguel Montero grounded into a double play.
The Braves went up 1-0 in the first when Jason Heyward doubled and scored from second on Justin Upton’s RBI single. Diamondbacks starter Randall Delgado avoided further damage with two runners in scoring position by striking out Dan Uggla.
Teheran stranded runners in scoring position in the first with strikeouts of Paul Goldschmidt and Miguel Montero and in the third with a strikeout of Gerardo Parra and Aaron Hill’s groundout.
Teheran, whose night ended when Tyler Pastornicky pinch-hit for him in the bottom of the sixth, has a 0.98 ERA in winning two of his last three starts.
Luis Avilan, the second Atlanta pitcher, threw five straight balls before Jason Kubel hit into a forceout and Cody Ross grounded into a double play.
Avilan retired the four batters he faced before Jordan Walden got the last two outs of the eighth.
Delgado (0-2) gave up eight hits, two runs and three walks. He struck out three and threw 64 of 106 pitches for strikes.
Delgado, whom Atlanta dealt with Martin Prado to Arizona in the trade that brought Justin Upton and Chris Johnson to the Braves in January, escaped a bases-loaded jam in the fourth when Teheran grounded into a double play.
Atlanta made it 2-0 in the fifth when Simmons’ sixth homer landed in the left-field seats.
Parra, Goldschmidt, Montero, Jason Kubel and Ross were a combined 0 for 16 with two walks and 10 strikeouts.
Former Kell High School ace Zeke Spruill, the fourth Arizona pitcher, gave up a leadoff triple to Dan Uggla, who scored on pinch-hitter Reed Johnson’s pinch-hit RBI bunt single to give the Braves a 3-0 lead.
NOTES: Arizona reinstated 3B Eric Chavez from the 15-day disabled list and designated INF Eric Hinske for assignment. Chavez had been on the DL since straining his right oblique on May 30 against Texas. Before the injury, he was hitting .325 with seven homers and 25 RBIs in 38 games after signing with the Diamondbacks during the offseason. ... Arizona manager Kirk Gibson said that RHP J.J. Putz is likely to be activated before today’s 4:05 p.m. game. ... The Braves improved to 42-9 when they hit a homer. ... Atlanta INF Ramiro Pena had season-ending surgery to repair a tear in the back of his right shoulder. Pena, a three-year veteran in his first season with the Braves, will be out until the start of spring training next year. ... Arizona hitting coach Don Baylor, who held the same role with Atlanta when Jones won his NL MVP award in 1999, celebrated his 64th birthday Friday. ... The Braves announced a sellout of 48,282, though several hundred seats were empty.