Hanson struck out on a key squeeze play with the bases loaded early in the game, as Dillon Gee and New York beat the Braves 3-2 on Sunday.
New York's new No. 2 hitter Josh Thole had two run-scoring singles as the Mets ended their seven-game losing streak.
Dan Uggla led off the second with a triple for the Braves. Following a walk to Eric Hinske, Uggla scored on Freddie Freeman's single.
The Braves loaded the bases following a single by Alex Gonzalez, but with one out Hanson whiffed on a squeeze play and Hinske was caught in a run-down between third base and home to end the inning.
Hanson said he struck out on a fastball from Gee.
"I don't know, when it was coming in, I didn't blink or anything, I didn't see it very well," Hanson said. "I just swung right through it."
The botched squeeze play proved costly.
"Little things like that, that play goes the other way, we're still playing and maybe have a chance to win the ball game right there," said Chipper Jones.
Atlanta's Jason Heyward hit a homer off Jason Isringhausen in the eighth before the Braves had another costly mistake. Brian McCann walked but was caught stealing.
Gee (1-0) gave up five hits and a run in 5 2/3 innings to beat Hanson (1-3).
Hanson gave up three runs on five hits and two walks.
Francisco Rodriguez pitched the ninth for his second save. Jones walked to lead off the ninth and was stranded on third when Rodriguez struck out pinch-hitter Brooks Conrad.
"We won the series, that's the most important thing," Jones said, calling the loss "obviously a little bit of a downer today."
Braves manager Fredi Gonzalez altered his lineup. Heyward hit second, Brian McCann hit third and Dan Uggla hit fourth.
Jones was given a break after playing both games of Saturday's doubleheader. Jones entered the game as a pinch-hitter in the sixth.
Some have suggested Heyward should hit in the No. 2 spot to take advantage of his .368 on-base percentage. He has hit sixth most of the season.
Heyward's homer to lead off the eighth was his fourth.
Mets manager Terry Collins also shook up the lineup, moving Thole, the Mets' catcher, up from the No. 8 spot to hit behind leadoff hitter Jose Reyes. Thole had run-scoring singles in the first and fifth innings.
The Mets bounced back after being swept in doubleheaders by the Braves on Saturday and by Colorado on Thursday.
Ike Davis drove in Thole with a single in the first inning.
Thole hit eighth in each of his previous 11 starts. Collins said he made the move to take advantage of Thole's discipline at the plate.
Gee was recalled from Triple-A Buffalo but had travel woes before finally arriving in Atlanta about 1 a.m. on Sunday.
Gee's baggage never arrived, so he had to borrow Thole's shoes and Bobby Parnell's glove.
"It's the same game out there, no matter what glove you've got," Gee said.
The Mets needed Gee after placing right-hander Chris Young on the 15-day disabled list Saturday with right biceps tendinitis.