Anand Shirodkar of the Goa Suraksha Manch came a distant third with 220 votes.
BJP's Sidharth Kuncolienkar had won the seat in 2014 bypoll and also in the 2017 election, but stepped down to make way for Parrikar's election from Panaji, which the chief minister represented from 1994 to November 2014.
Counting of votes in four assembly constituencies - Bawana in Delhi, Nandyal in Andhra Pradesh, Valpoi and Panaji in Goa got underway on Monday morning.
The BJP's defeat in Bawana just four months after its massive victory in MCD elections and one-sided win in Rajouri Garden bypolls is nearly like a U-turn by voters in Delhi.
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In Delhi, the by-election will decide the fate of candidates of the three major political parties - the ruling AAP, the BJP and the Congress - all of whom have exuded confidence about winning the Assembly seat reserved for the SC category.
After facing disappointments and drubbing in back-to-back Assembly polls in Punjab, Goa, Delhi civic polls and Rajouri Garden bypolls recently, the Aam Aadmi Party (AAP) supremo Arvind Kejriwal helped the party break the jinx and regained his party's glory by making a comeback in the Bawana bypolls on Monday.
Voting was conducted on 23 August at 379 polling booths.
"We want to thank all voters, supporters and leaders who helped in winning the seat", AAP leader and Delhi Deputy Chief Minister tweeted after the victory.
The by-election was held because Ved Prakash had to resign as a legislator after shifting to the BJP.
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Hindustan Times today reported a BJP insider as saying that there was an internal bickering in the party, which resulted in the loss.
Andhra Pradesh's ruling Telugu Desam Party (TDP) snatched the Nandyal Assembly seat by defeating YSR candidate with a huge margin.
The Nandyal by-poll was necessitated after the death of Bhuma Nagi Reddy, who had in fact quit the YSR Congress a year ago to join the ruling TDP. In the previous five elections, the Congress had struggled to go over even 5,000 votes.
Parrikar won the Panaji seat for the sixth time.
The fourth by-poll - for the Nandyal seat in Andhra Pradesh - nearly as keenly contested as the Bawana seat albeit with different players - was wrested by the ruling Telugu Desam Party (TDP) of chief minister N Chandrababu Naidu, drawing the curtains on a shrill election campaign that saw him and his principal rival - YSR Congress chief YS Jagan Mohan Reddy trade sharp exchanges. The Congress finished far behind with just 1,382 votes.
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