[2][3] Ueki came to fame through the comic jazz-band The Crazy Cats led by Hajime Hana.

His major appearances were in the Musekinin Otoko film series, the comedy variety show Shabondama Holiday, the prime-time television series The Hangman, and the ten 2-hour television shows in the Nagoya Yomeiri Monogatari franchise.

He appeared in the Akira Kurosawa epic jidaigeki film Ran in 1985, receiving a nomination for the Japan Academy Prize for Outstanding Performance by an Actor in a Supporting Role, and earned the Japanese Academy, Kinema Junpo, and Mainichi film awards for best supporting actor for his role as the eccentric grandfather in Big Joys, Small Sorrows in 1987.

His hit song with Hana Hajime and the Crazy Cats, Sūdara-bushi, placed in the Oricon top ten,[6] and landed him an appearance on the NHK annual music spectacular Kōhaku Uta Gassen.

Ueki received the Purple Ribbon Medal of Honour in 1993 and the 4th Class Order of the Rising Sun in 1999.