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Niese outpitched Hudson on a special night. A sellout crowd of 51,910 packed Turner Field for a pregame tribute to Jones.
Niese wasn't distracted.
"It was a special night for Chip," Niese said. "It couldn't go to a more deserving guy. He plays the game the right way. All the respect, all the accolades are deserved.
"It's always an honor to be able to face a player like that, a future Hall of Famer. To do it tonight in front of all those people was pretty special."
Niese (13-9) allowed one run and four hits in seven innings for his third straight win.
"When I walk off the mound and our team has a chance to win, then that's satisfaction," Niese said.
The Braves, who have wrapped up at least a wild-card berth, wasted an opportunity to gain ground in the NL East. Atlanta remained four games behind the first-place Nationals, who lost 12-2 to St. Louis.
"You feel like when Huddy gives you the performance he gave you that you have a chance, but we didn't score runs," Braves manager Fredi Gonzalez said.
Jones, starting his final regular-season home series before retiring, was 0 for 4 with four groundouts. Jones was honored by the Braves in a pregame ceremony that included former Atlanta manager Bobby Cox and Hall of Famer Hank Aaron.
Jones said the tribute, which included video messages from former teammates and such celebrities as Michael Jordan between innings, was overwhelming.
"I think I had a tear planted in the corner of my eye pretty much the whole night," Jones said.
"It was a little overwhelming, too overwhelming. ... There's no real way to prepare that that."
Jones said he hopes the focus returns to baseball for the last two games of the series.
"Everybody showed me such a great day," Jones said. "I wish I had played better. I wish we had played better.
"I'm glad it's over. ... I just want to concentrate on baseball. All the attention needs to take a backseat so we can focus on the job at hand."
Freddie Freeman gave Atlanta a 1-0 lead with his 23rd homer in the fourth.
Bobby Parnell pitched a perfect ninth for his sixth save.
Hudson (16-7) gave up only three hits in six scoreless innings before Daniel Murphy led off the seventh with a double to left field. Murphy advanced to third when Jason Heyward made a diving catch on David Wright's sinking liner in right.
"His credentials are unbelievable," Duda said of Hudson. "I'm happy to do anything I can.
"I was kind of nervous, two strikes. I just tried to make contact, get the ball up and it went out of the park."
Hudson allowed three runs, five hits and one walk in seven innings.
"It's frustrating. One pitch pretty much put a damper on my night," Hudson said.
"I didn't make a very good pitch right then. I felt it was the one bad pitch of the at-bat. You have to tip your cap to him."
The Mets loaded the bases with one out in the eighth against Cristhian Martinez. Cory Gearrin ended the inning on Wright's grounder to Jones, who stepped on third base before throwing to first for the double play.
In the pregame ceremony, Aaron gave Jones a third base with the words "Chipper Jones 1993-2012." The special bases with the tribute to Jones were used in the game. The on-deck circles also carried the logo, and Jones' No. 10 was painted in the grass in center field.
Braves players gave Jones a pool table. The team gave Jones and his family a trip to Hawaii and a plaque made from Turner Field bricks and shaped like home plate. Team president John Schuerholz announced Jones' clubhouse locker will be moved to Jones' home.
New York's Ruben Tejada hit the game's first pitch to Jones, who had a wide grin after making the pickup -- with a slight bobble -- and then throwing out the shortstop.
Before the at-bat, Jones said he warned Hudson he was "an emotional wreck." He asked Hudson to "keep the ball away from me."
Instead, Jones was immediately tested.
"That was probably the most nervous I've been on a baseball field in a long time," he said.
- The attendance was Atlanta's largest of the season and the seventh-biggest in Turner Field history.
- Mets manager Terry Collins said Parnell will serve as closer in the final week of the season. Frank Francisco (elbow tendinitis) leads the team with 23 saves but has not pitched since Sept. 16.
- Braves C Brian McCann (sore right knee, sore right shoulder) was held out for the second straight day.
- Gonzalez said CF Michael Bourn (slightly sprained left thumb) could return Saturday or Sunday after missing his fifth straight start.
- The series continues on Saturday night when Braves LHP Mike Minor (10-10) faces Mets RHP Chris Young (4-8).