Valverde loaded the basses in the ninth before Jason Heyward flied to the warning track in center field to end it.
Colon, 40, gave up six hits and no walks, struck out five and didn't allow more than one baserunner in any inning until the seventh as he outpitched Atlanta's Aaron Harang (1-1).
Travis d'Arnaud said catching Colon (1-1) is "a lot of fun."
"He commands all his pitches," d'Arnaud said. "What else could you ask for from a pitcher?"
Tejada scored on a wild pitch by Harang in the third and had run-scoring singles in the seventh and eighth innings.
The Braves honored the 40th anniversary of Hank Aaron's 715th homer in a pregame ceremony attended by baseball commissioner Bud Selig. Al Downing, the former Dodgers' left-hander who gave up the homer, attended the ceremony and threw out the first pitch.
There was little left to get excited about for the home crowd until the ninth.
Justin Upton and Dan Uggla had back-to-back singles off Valverde. Evan Gattis, who returned after missing two games -- and losing seven pounds -- because of a stomach virus, hit a fielder's choice grounder that forced Upton at third.
Valverde then fielded Andrelton Simmons' grounder, turned and threw wide of second base for an error, leaving the bases loaded. Pinch hitter Gerald Laird popped out to second base and Lagares caught Heyward's shot to end the game.
"I knew I just missed it," Heyward said. "I'd like to be in that spot every time. I'd like to come through."
Heyward, who was 0-for-5, is hitting .107.
Mets manager Terry Collins said the Braves had aggressive swings in the ninth because Valverde was throwing strikes.
"The ninth inning is a tough inning," Collins said.
"You've got a club like the Braves who swing the bats and this guy attacks the strike zone. They're gonna get some hits. When he starts missing is when he gets in trouble. When he throws strikes he gets outs because you've got to swing."
Valverde moved into the closer's role as the replacement for Bobby Parnell, who had season-ending Tommy John surgery on Tuesday.
Harang was hurt by control problems in an otherwise strong outing. He allowed only two hits with nine strikeouts in six innings, but he gave up four walks, including two in the third. Tejada led off with a walk and eventually scored on Harang's wild pitch to David Wright.
"I tried to put him away, a 2-2 count, I threw a slider in the dirt," Harang said. "It took an awkward bounce, got away from Evan.
"Other than that I felt good. I kept them off-balance. We just weren't able to work anything up on Colon tonight."
The Mets added two runs off Braves rookie Gus Schlosser in the seventh. Tejada and Young had run-scoring singles.
Braves left-hander Luis Avilan left the game in the seventh with a left hamstring cramp after he dodged Daniel Murphy's broken-bat on a single. Avilan was limping and was unable to make a warm-up throw but said after the game he did not expect to miss any time.
Braves RHP Cory Gearrin confirmed he will have season-ending Tommy John surgery. The Braves previously lost starting pitchers Kris Medlen and Brandon Beachy to season-ending elbow injuries this spring. ... RHP Ervin Santana will make his first start for the Braves on Wednesday after signing with the team on March 12. RHP Zack Wheeler will start for the Mets. ... The Mets said Parnell's right elbow ligament-replacement surgery, performed by Dr. David Altchek, was successful. The team announced plans for the surgery on Sunday.