Sunita (Asha Parekh) lives along with her widowed father in a rich neighborhood of Delhi. She is deeply disturbed by the suicide of her elder sister Roopa in Dehradun a year ago. All she knows was that Roopa committed suicide due to her involvement with a hotel live band drummer "Rocky". (a role played by Shammi Kapoor, who was repeating the drummers role from his 1959 blockbuster "Dil Deke Dekho", with the same co-star and director)

On the way to Dehradun, Sunita meets a charming but mischievous young man Anil (Shammi Kapoor) on the train. Anil gets attracted by Sunita's beauty and spirit and decides to pursue her. Later he overhears Sunita saying that she would definitely take revenge on "Rocky", who was the cause of her sister's suicide. Anil's stage name being "Rocky".

Narrating his version of what happened to his friend, he reveals that he was never interested in Roopa and she was the one who always pursued him. one evening telling him that she would be coming to his room in the hotel and if he did not open his door, she will jump and commit suicide. later that evening when she starts banging on his door, he does not open the door, and then he hears a shriek and a thud. When he rushes out and looks down from the 3rd floor lobby balcony (TEESRI MANZIL) he sees Roopa's body on the Compound below, apparently she having jumped as she had threatened.

He tries to explain everything to Sunita, but always postpones it. He takes the help of a rich patron of their hotel, Mr. Kunwer to pose as a rich heir in front of Sunita's father. But after some time, it is revealed that he was no one but Rocky. He tries to explain to Sunita but she wouldn't listen. His pursuit of Sunita's attention and affection, along with the hotel club backdrop, gives many a chance to break out in song and dance.

Police arrest Anil and later release him. To his surprise, they reveal that Roopa didn't commit suicide, but was murdered. A fact the police kept silent to catch the actual murderer. They also warn Anil that the killer might target him as he was closely linked to the case.

Anil suspects Ruby (Helen), his co-dancer and his admirer but she is murdered before his eyes and although he chases the killer, Anil is unable to catch him. He then suspects Ramesh (Prem Chopra), Roopa's fiance, but finds no clue. Later, police tells him that the murderer wanted to kill Anil, but Ruby came in between. A mysterious young woman calls him one night and asks him to go to a certain place in her car to know the truth about Roopa. But the car has been tampered with and goes of a cliff and with no body found, everybody thinks that Anil is dead. But he survives and investigates further and at last finds the actual killer and the motive behind Roopa's murder.

Anil and Sunita go to a hotel to investigate the mystery. When Sunita is away, Anil finds the mysterious lady going in a car. Anil follows her to the hotel owned by Mr Kunvar. The two men search for the lady, but are unable to find her.

Mr. Kunvar insists that Anil spend the night there and locks him in from outside. Anil discovers an important evidence for Roopa's murder. The killer is revealed to be Mr. Kunvar himself. Anil confronts the woman who is actually Kunvar's mistress. She confesses to the police about the crime. The mistress tells Anil that she was having relations with Kunvar when the latter was still married. Kunvar's wife discovered the affair and in the scuffle, Kunvar accidentally shot her dead. Kunvar and his mistress were burying the body in secret when Roopa witnessed everything. Kunvar chased her to the hotel and threw her from the higher floor, murdering her.

Kunvar arrives and kills his mistress. Anil and Kunvar fight each other and Anil overpowers him. The police arrive. Kunvar commits suicide. The film ends with Sunita and Anil together.

• Shammi Kapoor as Anil Kumar "Sona"/Rocky
• Asha Parekh as Sunita
• Prem Chopra as Ramesh
• Helen as Ruby
• Premnath as Kunvar Saab
• Ram Avtar as train passenger
• Iftekhar as Police Inspector
• Raj Mehra as Sunita's Dad
• Laxmi Chhaya as Bela
• Salim Khan as Rocky's Friend

Nasir Hussain produced and wrote the film under his home banner. He approached Dev Anand to star in Teesri Manzil and he immediately agreed. However, at the same time, another of Nasir Hussain's production Baharon Ke Sapne was to be directed by Vijay Anand. Then, on occasion of Sadhana's engagement party, a misunderstanding erupted between Dev Anand and Nasir Hussain, when apparently, Nasir overheard Dev Anand saying "The film which Nasir is making with me is coloured and he has given Goldie some black-and-white film to make. Goldie is making the movie with some new boy, Rajesh Khanna". It was the next day that Nasir requested Vijay Anand to direct Teezri Manzil and offered to helm Baharon Ke Sapne, but specified that Teesri Manzil would not have Dev Anand in it. It was only then that Shammi Kapoor was approached. Vijay came on board to direct and edit the film. Hussain then cast Shammi Kapoor, who had earlier starred in Hussain's two big hits Tumsa Nahin Dekha (1957) and Dil Deke Dekho, which introduced Asha Parekh. Asha had starred in two more hits for Hussain Jab Pyar Kisise Hota Hai (1961) and Phir Wohi Dil Laya Hoon (1963). Thus, the newcomer for this film would be music composer R.D. Burman (son of music composer S.D. Burman), and he would create phenomenal music for this film. He would compose for all of Hussain's films until Zabardast (1985). Shammi Kapoor, Hussain and Vijay individually took credit for discovering the supremely talented R.D. Burman. But R.D. Burman gave credit to lyricist Majrooh Sultanpuri for recommending him to Hussain, and both of them would create unforgettable songs for Teesri Manzil. All the hit songs featured the excellent Mohammed Rafi^[4] The song picturizations were outstanding, with Helen dancing to "Oh Haseena Zulfon Waali". Songs such as "Aaja aaja" had a rock n' roll base and were extremely popular.

All the songs^[5] were composed by Rahul Dev Burman and lyrics were penned by Majrooh Sultanpuri. The excellent Mohammed Rafi featured in all the songs. Choreography was by Herman Benjamin.^[6]

The film became a hit and remains popular to this day. Although it is a murder mystery, it continues to draw repeat audiences, even though the identity of the murderer is no longer a secret. Teesri Manzil was the last time Shammi starred in a Nasir Hussain film. Asha would go on to do four more, three of which she starred in.

Teesri Manzil was also the last Hussain film in which Mohammed Rafi sang all the songs. By Yaadon Ki Baraat, Kishore Kumar had temporarily become the dominant singer in Hussain's movies, but Rafi always had a special place in Hussain's films and would later win major awards for the song "Kya Hua Tera Wada" in Hussain's Hum Kisise Kum Naheen (1977).

Hussain and Vijay never worked together after Teesri Manzil. Hussain would return to directing all his films again and would only relinquish the director's chair to his son after three of his films flopped in the 1980s. Salim Khan played a small role as Shammi Kapoor's musician friend who pretends to be Rocky in the musical number "Oh Haseena Zulfon Waali". In real life, Helen would later become his second wife. Shammi's wife Geeta Bali died during the filming, and Vijay helped Shammi get over the grief.^[7]