Asrani was born into a middle-class Sindhi family. His father migrated to Jaipur after the Partition of India and established a carpet shop. Asrani was one of seven siblings, with four sisters and three brothers, two of whom were elder and one younger. He was disinterested in business and struggled with mathematics, but his ultimate goal was to become an actor.
Asrani began his acting journey by learning from Sahitya Kalbhai Thakkar from 1960 to 1962. He then traveled to Bombay in 1962 and began seeking opportunities to act. Hrishikesh Mukherjee advised him to pursue professional acting training, which he did at the Film Institute in Poona (now Film and Television Institute of India, Pune) from 1964 to 1966. He impressed many and made his acting break in 1967 with a Gujarati movie opposite budding actress Waheeda.
Asrani's debut film in Hindi was Hare Kaanch Ki Chudiyaan, where he appeared as Biswajeet's friend. He acted in Khoon Pasina, marking a serious role beyond comedy. He started getting more offers as the main comedian in films or as the close friend of the lead actor from 1971. He worked with directors like Hrishikesh Mukherjee, Atma Ram, and Gulzar repeatedly from 1971 to 1974, and his work received notice through these hits.
Asrani's roles in the 1970s set the tone for a number of supporting and comic roles in his career. He was in high demand, appearing in 101 films from 1970 to 1979, and had effective roles in them. He was a close friend of Rajesh Khanna and worked with him in 25 films, including 21 hits.
In the 1980s, Asrani acted in over 107 films. His roles were mostly minor, as the concept of a comedian was getting phased out, and heroes preferred to do their own comedy and action films were ruling the roost. Simultaneously, he kept working in Gujarati films, achieving success as the lead protagonist in Amdavad No Rikshawalo, Saat Qaidi, Sansar Chakra, Pankhi No Malo, Jugal Jodi, Maa Baap, and Chel Chabilo Gujarati.
From the 1990s, Asrani played as a comedian or supporting actor in Gujarati films like Mota Ghar Ni Vahu, Piyu Gayo Pardesh, Baap Dhamal Dikhra. He set up a small Gujarati production company with fellow artistes Dinesh Hingoo, Harish Patel, and Salim Parvez in 1982, which dissolved in 1996 with a large profit. Asrani also invested in cloth and acted as an investor for other actors until 1991, when he lost a lot of money.
From 1988 to 1993, Asrani was a director for the Film Institute in Pune. In the 1990s, he did only 73 Hindi movies due to lack of good scope for him to perform. Muqabla (1993) saw him in a serious role after a long time. D.Rama Naidu gave him a pivotal role in Taqdeerwala in 1995, and once again comedy movies were being made from thereon.
Asrani started getting good roles in films directed by David Dhawan and Priyadarshan from 1993 till 2012. The 2000s saw Asrani in a number of blockbuster films like Hera Pheri, Chup Chup Ke, Hulchul, and Deewane Huye Pagal. He appeared in a serious role in Kyun Ki. He was an integral part of comedies by Sajid Nadiadwala, Priyadarshan after 2000.
Asrani's screen space in films of Rohit Shetty and others has gradually reduced after 2009. He worked in a Bagheli film for the first time by playing the role of a Ticket Conductor (TC) in superstar Avinash Tiwari's film 'Kunwarapur' (2024).