Jurrjens (8-3), who began the night with the best ERA in the majors at 1.82, set season highs with five walks while allowing eight hits and four runs in 5 1-3 innings.
Reyes' 34th multihit game — tops in the majors — helped Jonathon Niese (6-5) win his third straight decision. Niese allowed two runs on five hits and no walks in 6 1-3 innings.
Dan Uggla's homer off Jason Isringhausen in the eighth cut the Mets' lead to 4-3. Chipper Jones followed with a long drive that a leaping Carlos Beltran caught in front of the right-field wall.
Francisco Rodriguez pitched a perfect ninth for his 19th save as the Mets won for the eighth time in 12 games.
Reyes led off the game with an infield hit and then, slipping in the thick, wet dirt beside first base, barely made it back to the bag on two pickoff attempts from Jurrjens. First base umpire Bill Miller and crew chief Tom Hallion called for dry dirt to be added to the base path, too soggy from pregame watering.
Reyes then stole second and scored on Beltran's single to center.
Reyes and Willie Harris had singles in the third before advancing with a double-steal. Jurrjens' walk to Daniel Murphy loaded the bases. Angel Pagan's single to right drove in Reyes, and Harris scored on Lucas Duda's flyball to center for a 3-1 lead.
Reyes, hitting .346, added a run-scoring single off Jurrjens in the sixth.
Joe Mather singled in David Ross in the second for Atlanta. Ross knocked Niese out of the game with a run-scoring double in the seventh.
Jurrjens has allowed more than two runs in only two of his 12 starts this season — both against the Mets. The right-hander gave up four runs, three earned, in a 5-0 loss at New York on June 4.
Braves closer Craig Kimbrel loaded the bases in the ninth with two walks and a hit batter before striking out Ruben Tejada to end the inning.
First baseman Freddie Freeman was scratched from Atlanta's lineup with a mild right oblique strain, leaving the Braves without five regulars. Three starting outfielders — Jason Heyward, Nate McLouth and Martin Prado — are on the disabled list. Catcher Brian McCann didn't start, but remained in the game after striking out as a pinch-hitter in the seventh.
Freeman is listed as day to day.
Notes: Mets 3B Justin Turner is expected to miss a couple of days with swelling in his right hand. Turner said he hurt his hand when he was jammed at the plate. Murphy started at third base. ... Manager Terry Collins said he didn't start slumping OF Jason Bay because right-handed hitters struggle against Jurrjens. Collins didn't commit to Bay returning to the lineup Wednesday. ... After striking out as a pinch-hitter in the seventh, Diory Hernandez remained in the game to play first base for the first time in three seasons. ... Heyward, with Triple-A Gwinnett on a rehab assignment, could return from his right shoulder injury as soon as Wednesday.