Hasrat was born Iqbal Husain in Jaipur, where he studied English till medium level, and then acquired his taalim in Urdu and Persian from his grandfather, Fida Husain. He began writing verse, when he was around twenty years old. Around same time, he fell in love with a Hindu girl named Radha. He wrote a poem for her;
Yeh mera prem patra padh kar,
ke tum naaraaz na hona.
Later, the poem was used as a song in Raj Kapoor's film, Sangam (1964).
In 1940, Hasrat came to Bombay (now Mumbai), and worked as a bus conductor, earning a monthly salary of eleven rupees. He used to participate in mushairas. At a mushaira, Prithviraj Kapoor noticed Hasrat and recommended him to his son, Raj Kapoor. Raj Kapoor was planning a musical love story, Barsaat (1949) with Shankar-Jaikishan. Hasrat wrote his first recorded song, Jiya Beqaraar Hai for the film. His second song (and first duet) was Chhod Gaye Baalam.
Along with Shailendra, Hasrat wrote lyrics for all Raj Kapoor films till 1971. But after the death of Jaikishan, and failures of Mera Naam Joker and Kal Aaj Aur Kal, Raj Kapoor turned to other lyricists and music directors. Kapoor initially wanted to call him back for Prem Rog, but later settled for another lyricist, Amir Qazalbash. Kapoor finally asked him to write lyrics for the film, Ram Teri Ganga Maili. Later, he also invited him to write three songs for the movie Henna. Hasrat alleges that after Raj Kapoor's death, the music composer Ravindra Jain "conspired" to "scrap" his lyrics and replace them with his own lyrics.
When fellow lyricist Shailendra turned producer with Teesri Kasam, he invited Hasrat to write lyrics for the movie. He also wrote screenplay for the movie Hulchul (1951). His last film as a lyricist was Hatya: The Murder (2004).
Hasrat has written several books of poetry, in Hindi and Urdu. He once said, "Hindi and Urdu are like two great and inseparable sisters".
Hasrat Jaipuri invested his earnings in property, on his wife's advice. Thanks to earnings from these properties, his financial condition was sound, and therefore he was not much active as a lyricist. He was survived by two sons and a daughter.