The Mets needed almost all of them to hold off the homer-happy Atlanta Braves.
Alonso drove in six runs with five hits, including a three-run homer that helped lead to Julio Teheran's shortest career start, and the Mets held on in the ninth inning to beat the Braves 10-8.
"It's incredible. It's hard to put in words, five knocks as a rookie," Mets starter Marcus Stroman said of Alonso. "It seems like he's on everything, barreling everything."
Alonso's first-inning homer carried 451 feet before making a splash landing in the pool behind the center-field wall.
Alonso's 39th homer tied Cody Bellinger for the National League rookie record. Bellinger hit 39 homers for the Dodgers in 2017, the same year the Yankees' Aaron Judge set the major league rookie mark with 52.
"I don't stand alone," Alonso said. "I'm tied. Hopefully I keep on going and keep pushing forward. Hopefully I can stand alone in that category."
Alonso set career single-game highs for hits and RBIs.
The Mets had a season-best 23 hits. Rosario's career-high five hits included two doubles, two singles and a triple. It was the first time in franchise history the Mets had more than one player with five hits.
"That's nuts. That's crazy," Alonso said when told about the duo making history. "I think all of us kind of fed off Amed today."
Wilson Ramos added four hits.
New York won despite giving up six homers, including three in the ninth. Freddie Freeman and Josh Donaldson each hit his second homer of the game in the inning and Ronald Acuna Jr. hit a two-run shot -- all against Drew Gagnon.
Stroman (7-11) allowed three runs, two earned, on four hits in 5⅓ innings. The right-hander earned his first win in three starts since being traded to New York from Toronto on July 28.
Stroman gave up homers to Matt Joyce in the fourth and Donaldson in the sixth.
New York, trying to stay close in the NL wild-card race, snapped a three-game losing streak that included the first two games of the series.
Teheran (7-8) walked three consecutive batters to force in a run in the second. He left the game after giving up a run-scoring single to Ramos. Teheran recorded only four outs while giving up eight hits and six runs.
"My command wasn't there," Teheran said, adding he'll try to quickly move past the ugly outing. "I'm just going to put it in a bag and concentrate on the next one."
Alonso drove in two runs with a fifth-inning single off Tomlin and added a run-scoring single off Anthony Swarzak in the seventh.
Mets: Only one day after he was placed on the 10-day injured list with a mild left hamstring strain, 2B Jeff McNeil jogged in the outfield before batting practice. McNeil said he hopes he won't miss more than 10 days with his second IL stint this season with the same injury.
Braves: SS Dansby Swanson (right foot contusion) hasn't been cleared to run but took fielding practice from his knees before the game. It's the same drill regularly used by third-base coach Ron Washington with infielders. Swanson, who also played catch in the outfield, has been out since July 24.
Teheran fell to 1-2 in four starts against the Mets this season, including three straight in which he failed to last longer than four innings.
CATCH OF THE DAY
Acuna robbed J.D. Davis of a homer in the sixth by leaping and reaching above the yellow line atop the left-field wall for a catch. Acuna landed in a sitting position on the warning track before pausing and throwing the ball back to the infield as fans cheered.
"Kind of dramatic," Braves manager Brian Snitker said of the brief uncertainty about the catch. "Good for him. It's entertainment."
Mets: RHP Noah Syndergaard (8-5, 3.89 ERA) will make his first start against the Royals since 2016 when the Mets open a three-game series at Kansas City on Friday night. Syndergaard gave up three runs in six innings in a 4-3 win in the 2016 start.
Braves: RHP Mike Soroka (10-2, 2.32) will make his first start against Los Angeles when Atlanta opens a three-game series against Kenta Maeda and the Dodgers on Friday night. The matchup of division leaders is a rematch of the 2018 NL Division Series won by the Dodgers.
Greinke finally gets win over old club, Astros top Royals
Zack Greinke finally beat his old club and Yordan Alvarez belted a pinch-hit three-run homer as the Houston Astros beat the Kansas City Royals 6-1 on Saturday night.
Diamondbacks snap 6-game skid with 1-0 win over Reds
Merrill Kelly pitched seven scoreless innings, Nick Ahmed's triple led to the game's only run and the Arizona Diamondbacks snapped a six-game losing streak by beating the Cincinnati Reds 1-0 on Saturday night.
Benintendi's sac fly lifts Red Sox past Phillies 2-1
Pinch-hitter Andrew Benintendi's sacrifice fly in the top of the ninth inning lifted the Boston Red Sox to a 2-1 win over the Philadelphia Phillies on Saturday night.
Hicks, Reyes power Tigers past Orioles in 12 innings 8-4
Victor Reyes hit a tying home run with two outs in the ninth inning and John Hicks had the game-winning grand slam in the 12th to lift the Detroit Tigers to an 8-4 victory over the Baltimore Orioles on Saturday.
Tigers walk off on Hicks' grand slam
John Hicks breaks the tie in the bottom of the 12th inning with a walk-off grand slam to lift Detroit past Baltimore.
Sanó's grand slam leads Twins to sweep of Indians
Miguel Sano's grand slam capped a five-run eighth inning and the Minnesota Twins grabbed firm control of the AL Central by beating the Cleveland Indians 9-5, completing a sweep of Saturday's day-night doubleheader.