Alonso belted a 418-foot homer off Kansas City Royals pitcher Jacob Barnes in the ninth inning. The solo shot broke a tie with Los Angeles Dodgers slugger Cody Bellinger for most home runs by an NL rookie in one season.
Bellinger, who has an MLB-leading 42 home runs this season, hit 39 homers in the 2017 campaign to set the previous single-season rookie mark.
"It's crazy. I don't even know," Alonso told reporters. "It's something that, coming into camp I didn't know if I was going to make the team or not. To break this record and have a good season and keep playing the way I've been playing to try to help this team win, this season's been unbelievable. It's been a dream come true so far."
Alonso also became the first Mets player to record 40 home runs in a single season since Carlos Beltran in 2016.
The Mets defeated the Royals 11-5 to pull the team into a three-way tie in the National League wild-card race. New York is 1 1/2 games behind the Chicago Cubs, who play the Pittsburgh Pirates on Sunday night.
The Cubs hold the second wild-card spot, while the Washington Nationals sit atop the NL wild-card standings.