The Braves have won 20 of 24 at Turner Field to improve the major leagues' best home record to 51-19.
Gattis, who was recalled earlier in the day after a three-game stint at Triple-A Gwinnett, tied it at 1-all off with his 16th homer in the seventh. After Mets starter Carlos Torres (3-3) walked Dan Uggla on nine pitches, Simmons hit his 13th homer to make it 3-1.
Medlen (12-12) allowed seven hits and one run while striking out nine.
Closer Craig Kimbrel converted his 34th straight save opportunity and improved to 44 for 47 this season. He struck out Juan Lagares and Matt den Dekker, allowed a single to Omar Quintanilla and retired pinch-hitter Justin Turner on a groundout.
New York has dropped three straight and nine of 13.
Torres gave up seven hits, three runs and one walk. Torres tied career highs with six strikeouts and seven innings pitched.
The Mets took a 1-0 lead in the sixth on Daniel Murphy's RBI double with one out, but Medlen limited the damage on Josh Satin's groundout and Lucas Duda's strikeout.
In the seventh, New York manager Terry Collins let Torres bat with runners at first and third, but the pitcher struck out.
Torres lost the lead in the bottom half of the inning, unable to finish off Gattis and Uggla when both hitters fell behind with 0-2 counts.
Medlen erased the first two runners in scoring position — Eric Young Jr. in the first and Duda in the fourth. Young tripled over Gattis' head in left field in the sixth and scored on Murphy's double. Medlen escaped further damage when Josh Satin grounded out and Duda took a called third strike.
Duda doubled with two out in the fourth, getting stranded on d'Arnaud's strikeout, but his average dropped to .169 in 59 at-bats with runners in scoring position.
Gattis, who went 3 for 3, spent the previous three days at Triple-A Gwinnett to get some at-bats. The NL's rookie of the month winner for April and May had slumped in August, but he seemed to correct his issues by going 6 for 13 in three games at Gwinnett.
Atlanta has won 29 of its last 38 games and has rallied for 41 victories, best in the NL.