The three accused teenagers had taken Shiva, a class XII student, to Murthal on the pretext of having dinner and killed him, before setting his body ablaze to hide his identity.
Police said Shiva was murdered by the teenagers as he had once abused his juvenile classmate.
The juvenile and the two other accused -- Varun Jindal (19) and Parth (19) -- were apprehended from north-west Delhi's Pitam Pura here today.
Shiva (18) had gone missing after he went to meet his friends in outer Delhi's Rohini on the intervening night of October 11 and October 12. His partially burnt body was recovered from near Murthal the next day.
As per Shiva's family, he left home on the evening of October 11 to meet his friends at a mall in Rohini after he received a phone call.
As he did not return, a missing report was filed by Shiva's parents and police started investigating the case.
"We came to know that the boy had gone with the three teenagers. They were apprehended from their residences in northeast Delhi's Pitam Pura today. During questioning they confessed to have killed the boy as he had abused his juvenile classmate once," said a senior police official.
On the fateful night, the teenagers met at the mall from where they left in a car to Murthal village in the Sonepat district of Haryana for dinner at a dhaba.
After dinner, the trio took Shiva to a secluded location, where they first allegedly strangulated him and then shot him with a gun before setting his body ablaze, police said.
"It has emerged that the juvenile, who was a friend and classmate of the victim, was the mastermind behind the whole plan. However, it is still to be known from where they had acquired the gun by which Shiva was allegedly shot," said DCP (Outer) Vikramjit Singh.