Balentien matched the mark set by Sadaharu Oh in 1964 and equaled by ex-major leaguers Tuffy Rhodes in 2001 and Alex Cabrera in 2002. He has 21 regular-season games left to break the record.
Balentien hit a solo homer in the sixth inning at Jingu Stadium and was presented with a bouquet of flowers after reaching home plate. Despite Balentien's home run, the Yakult Swallows lost 6-2 to the Hiroshima Carp.
"It's an honor to be tied with such great players," Balentien said. "I'm relieved and happy I was able to do it here in front of our home fans."
Balentien, who is from Curacao, played for the Mariners and Cincinnati Reds before signing with the Swallows in 2011. He hit 31 homers in each of his first two seasons in Japan.
Rhodes and Cabrera tied Oh's record with several games left but were then walked more and were unable to break it.
Oh is a legend in Japan. His 868 career home runs, which surpassed Hank Aaron's then major-league record of 755, made him a national hero.
The single-season home run record is also highly regarded, and former New York Yankees outfielder Hideki Matsui wore No. 55 in recognition of it.
The closest Matsui got to breaking Oh's record was 50 homers in 2002, when he played for the Yomiuri Giants.
The 29-year-old Balentien missed the first 12 games of this season because of a leg injury sustained while playing for the Netherlands in the World Baseball Classic.
Balentien's challenge of Oh's record comes in a season in which there is controversy over a new, livelier baseball.
In June, Japanese baseball officials admitted they introduced the new official ball this season without notifying players. The new ball has resulted in a dramatic increase in home runs.
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