Choudhry polled 64 out of a total of 112 votes polled while Dutt got 48.
Last year also, BJP candidate Savita Gupta had won the election bagging 66 votes.
In the house of 104 councillors, BJP is the single largest group with 44 members and has the support of BSP (6), INLD (3), JDU (1), besides a majority of the 14 independents.
Congress has 29, NCP 14 and RLD and SP one each.
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From Congress, MPs Parvez Hashmi, Ramesh Kumar, Sandeep Dikshit and Mahabal Mishra and Minister Arvinder Singh Lovely voted. BJP MLAs H S Balli, Satprakash Rana and V K Malhotra exercised their franchise.
With Choudhry's victory, BJP has won the Mayor election in all the three municipal corporations in the capital.
BJP's Azad Singh and Ram Narain Dubey have won the elections for mayor post in North Delhi and East Delhi corporations respectively.