The two wanted to marry but the girl Vimal's father Edward was opposed to it as Hari was already married.
On Friday night, when the father found the two together, police say he and one of his friends killed them.
"They were murdered in an under-construction building. Then the bodies were dumped in a park," said Rajan Bhagat, the PRO of Delhi Police.
"Children playing cricket in the park discovered the dead bodies," said Shri Ram, a resident of the area.
Vimal worked as a maid. Her father, a security guard, and his friend have been arrested. This is the third murder carried out in the name of honour in Delhi in recent months.
"You expect such things to happen in rural areas in Punjab and Haryana but not in Delhi, specially not in this area," said a shocked resident of the area.
The Law Minister has repeatedly stated that the government will soon introduce a new law to deal with cases of 'dishonour killings'. But the biggest challenge before the law enforcement agencies and the government is to deal with the social mindset that sanctions and justifies these heinous crimes.