Randhawa finished with a five-under-par 67 along with compatriot Mukesh Kumar after the opening round.
Randhawa finished with a five-under-par 67 along with compatriot Mukesh Kumar after the opening round of the $400,000 Asian Tour event which was delayed by thick fog for four hours in the morning before fading light brought an early end to the day's proceedings.
Thailand's Sutijet Kooratanapisan shot a 70 to sit in third place alongside a host of players who will return on Friday morning to complete their opening rounds.
Defending champion Chiragh Kumar of India returned with a 71 to stay four shots off the pace at the Delhi Golf Club.
Randhawa, the former Asian number one, continued his recent run of fine form for a solid start at a venue where he has won four Asian Tour titles previously.
"This is one of my favourite golf courses. I have a lot of good memories," said Randhawa, 44.
"I had a good finish to the round which was great. I have been playing a lot recently. I think that got me the good form," said the golfer, who enjoyed a top-five finish in the Philippines last month.
Randhawa also said he used the fog disruption to grab a couple of hours' sleep and a massage.
"I felt fresh when I started the round," said the eight-time Asian Tour winner.
After turning in 35, Randhawa sank two birdies against a bogey before blasting three straight birdies from 16 for a back-nine 32.
Kumar, a local veteran who has won over 120 professional titles in his career, took advantage of his knowledge of the course to ensure a fine start.
"I made a good recovery from the bushes on the sixth where I drained a 15-footer for bogey," said Kumar, who traded seven birdies against two bogeys.
Leading completed scores after first round (par 72):
67 - Jyoti Randhawa (IND), Mukesh Kumar (IND)
70 - Sutijet Kooratanapisan (THA)
71 - Sanjeev Kumar (IND), Chiragh Kumar (IND), Brett Munson (USA), Chikkarangappa S. (IND), M Dharma (IND), Shankar Das (IND), Vikrant Chopra (IND), Manav Jaini (IND), Gaurav Pratap Singh (IND).
72 - Abhishek Jha (IND), Chan Yih-shin (TPE), Abhinav Lohan (IND), Zamal Hossain Mollah (BAN), Simon Yates (SCO), Arie Irawan (MAS), Mardan Mamat (SIN), Om Prakash Chouhan (IND), Rahul Bajaj (IND), Sung Lee (KOR).