The Braves lead the NL East by 10 games over Washington. Atlanta opens a three-game series at Nationals Park on Monday night, and can clinch the division by winning twice there.
Smith (1-1) held the Braves hitless until pitcher Julio Teheran singled to lead off the sixth.
Smith allowed three hits and walked two. The rookie made his fifth career start -- he had a 12.41 ERA in his previous starts. He struck out seven of the first 13 Atlanta batters and credited catcher Nick Hundley with calling a good game.
"We had a pretty good rhythm going," Smith said. "Actually the only time I shook him off was that first hit off the pitcher. I probably shouldn't have done that."
Teheran (12-8) gave up seven hits, four runs, no walks and struck out six in 6 2/3 innings. Manager Fredi Gonzalez pulled him with two outs in the seventh after Burch bunted into a forceout.
Jedd Gyorko's RBI single and Headley's 13th homer in the sixth gave the Padres a 3-0 lead.
Medica, who homered off Philadelphia's Cliff Lee last Wednesday for his first career hit, led off the seventh with his second homer to make it 4-0.
Even though the slider he threw to Headley landed in the right-field seats, Teheran didn't regret the pitch selection.
"Yeah that was the pitch that I wanted to throw," Teheran said. "I asked him also if it was a good pitch (as Teheran stood at third base in the bottom half of the inning), and he told me that it was a good pitch. I said, `OK, you got me this time.' "
After Teheran left, reliever Scott Downs gave up a double to Will Venable that advanced Burch to third. After pinch-hitter Chris Denorfia walked to load the bases, Downs struck out Gyorko to end the threat.
Smith retired the first 11 batters before Freddie Freeman walked in the fourth. Freeman moved to second when Smith made a wild pickoff throw, but Evan Gattis struck out.
Padres closer Huston Street pitched the ninth. He gave up a leadoff single to Freeman before retiring the next three batters.
Teheran had retired 14 straight batters before Venable singled to begin the sixth. One out later, Venable stole second and scored on Gyorko's single.
Gonzalez was disappointed that the Braves' bats were quiet most of the weekend. Atlanta scored just three runs in the series and lost two of three.
"I thought (Teheran) pitched well enough for him to deserve a better opportunity to win the ballgame, if that makes any sense," Gonzalez said. "He gives up four runs, and I've seen our club at times score six, and he gets the win. We didn't do that today for him."
For Smith, the afternoon couldn't have gone much better, setting career highs in strikeouts, innings and earning his first win.
"It's good to get that out of the way," Smith said. "I don't have that hanging over my head anymore."
In the first six games of San Diego's 10-game road trip, Headley is hitting .364 with three homers and seven RBIs in 22 at-bats. ... Venable, who went 3 for 4, became the 10th San Diego player to have a 20 homer-20 steal season. The last Padre to accomplish the feat was Mike Cameron in 2006. ... Gattis went 0 for 4 and is hitless in his last 15 at-bats. ... Medica has hit safely in his first five games, batting .316 with three RBIs in 19 at-bats. ... Teheran didn't walk a batter for the first time since June 21 at Milwaukee, a span of 13 starts. ... Braves CF B.J. Upton, who went 0 for 3 and struck out twice, is 1 for his last 21. His average dropped one point to .190. Upton has struck out 143 times in 378 at-bats.
Copyright by STATS LLC and The Associated Press
ATLANTA, GA - SEPTEMBER 15: General view of seating at Turner Field prior to the game between the Atlanta Braves...