Ozzie Albies and Abraham Almonte also had two-run homers for the Braves, who have won two of three in a five-game series as they chase the first-place Mets in the NL East. Atlanta split Monday's doubleheader despite allowing just one run in two games.
"Three previous games we've given up three runs and were 1-2," manager Brian Snitker said. "So it was nice to come out and score some runs."
Dansby Swanson delivered a two-run double in the first inning to get Atlanta started.
Charlie Morton (10-3) earned the win after allowing three runs and five hits with five strikeouts over five innings.
Jeff McNeil and Brandon Drury each hit a two-run homer for the Mets after they trailed 10-1 in the fourth.
Riley's fourth-inning slam bounced off advertising signage near the left field foul pole and into a small seating overhang. His sixth-inning homer glanced off signage a few dozen feet to the right of his first round-tripper.
Riley has four homers in the last five games to increase his season total to a career-high 19, one more than he had as a rookie in 2018.
"The power's unbelievable," Snitker said of the 24-year-old Riley. "He's still figuring things out. He's learning. Getting all these at-bats are just going to do him well. He's a young hitter. Still a lot of upside in this guy."
The two-homer game was the third of the season and career for Riley, who had two homers May 21 against Pittsburgh and went deep twice again — this time with five RBIs — against the Pirates two days later.
Riley also continued a strong defensive series at third base in the third inning, when he saved a run by snaring a hard-hit grounder by McNeil and throwing to second to force Brandon Nimmo. During the Braves' 2-0 win in the first game of Monday's doubleheader, Riley grabbed a high chopper off the bat of Pete Alonso to begin a fifth-inning double play.
"The name of the game is just being consistent on both sides of the line," Riley said. "It's great to make good plays for your pitches. I know they love it."
Every starter for the Braves had at least one hit except catcher Stephen Vogt.
Riley's grand slam punctuated a rough night for Mets spot starter Jerad Eickhoff (0-2), who gave up 10 runs on seven hits and five walks in 3 1/3 innings. Eickhoff became the sixth pitcher in team history to allow 10 earned runs in an outing and the first since Johan Santana on May 2, 2010.
"I just feel frustrated — I let these guys down," Eickhoff said. "They're playing the Braves, obviously right behind you in the hunt for the division here. So it's frustrating. It's embarrassing."
Alonso had an RBI single in the third, McNeil extended his hitting streak to a career-high 14 games and Drury went 3 for 3 after entering in the fourth.
BACK AND FORTH
Eickhoff's rough start came hours after he joined the Mets for the third time this season. The right-hander was selected from Triple-A Syracuse on June 20 and posted a 4.50 ERA in two starts before being designated for assignment June 29. He remained with the organization and was called up again from Syracuse on July 11. After two appearances, he was again designated for assignment July 20 and opted for free agency before returning to the Mets.
"He came in and was ready to go for us," Mets manager Luis Rojas said. "I've seen him as a strike-thrower and he wasn't a strike-thrower tonight, maybe because of all the things he's gone through in the week."
The Braves have scored at least 10 runs in a game twice against the Mets in each of the last three seasons and nine times since 2018, tied for the most 10-run games they have enjoyed against any opponent in that span. Atlanta also has scored at least 10 runs nine times against the Philadelphia Phillies.
Braves: OF Joc Pederson (upset stomach) was scratched from the lineup less than an hour before first pitch. … RHP Huascar Ynoa (broken right hand) threw a simulated game at the Braves' minor league complex. … C Travis d'Arnaud (left thumb) ran the bases during batting practice and is scheduled to begin a rehab assignment this week.
Mets: RHP Jacob deGrom (right forearm) threw a side session, his second since being placed on the injured list July 18. … RHP Noah Syndergaard (Tommy John surgery) threw a bullpen for the first time since he was diagnosed with right elbow inflammation following a rehab start May 25. … RHP Carlos Carrasco (right hamstring) is expected to make his Mets debut Friday.
Braves: LHP Max Fried (7-6, 4.46 ERA) has recorded a decision in each of his last 11 starts (6-5), the longest streak by a Braves pitcher since Mike Foltynewicz earned 11 straight decisions in 2017.
Mets: Rookie RHP Tylor Megill (1-0, 2.10) has allowed one run or fewer four times in six outings, tied with Jim McAndrew (1968) for the most by a pitcher through his first six starts for the Mets.
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