You're My Pet(2000)

Kimi wa Pet

Life was good for Sumire Iwaya... until the day she discovers her boyfriend is cheating on her, she gets demoted at work, and her life spirals toward the dumps. Things take a turn for the better when she crosses paths with Momo, a homeless guy with a colorful past who puts a bounce in her step and a shake in her hips. It takes two to tango, but when Sumire's first love reappears in her life, will this be the last waltz?

(Source: Kodansha USA)

Note: won the 27th Kodansha Manga Award for shoujo (2003).