Uchiyama made his Davis Cup debut for Japan in February 2013, in the Asia/Oceania Zone Group I first round against Indonesia in Tokyo.

In the 2014 Davis Cup World Group first round against Canada in Tokyo, he played the doubles rubber with partner Kei Nishikori, winning over Canadian pair Daniel Nestor and Frank Dancevic.

[5] He reached the final of the Lexington Challenger in August 2015, losing to John Millman in three sets.

He qualified on his seventh attempt at the 2019 Japan Open, his home tournament, and reached his second ATP Tour quarterfinal (after 2019 Brisbane) with wins over Benoît Paire and Radu Albot.

160 at the 2024 Hangzhou Open, he reached the main draw as a qualifier, and then defeated lucky loser James McCabe and upset top seed Holger Rune, for his second top 20 and joint biggest career win (with world No.