The 31-year-old made a slow start to the Indian Premier League season following his move to Chennai from Rajasthan Royals, managing scores of only six, seven and nine in the straight defeats.
However, he produced a commanding innings featuring 15 fours and four sixes after Chennai were put in to bat, and received strong support from 18-year-old Ayush Mhatre, who was retired out for 59 off 36 balls.
Chennai posted 212-2 in their 20 overs, with Delhi managing only 189 in reply.
"To be very honest, how much form you're in, however many matches you have won for your country, a couple of failures definitely put a lot of doubts in your mind," Samson said at the post-match presentation.
"But I just wanted to go back and do my basics and believe in myself and just stick to my scoring patterns."
Samson registered the fourth century of his IPL career and delivered Chennai their first win of the season, easing the pressure on the five-time champions who were again without injured former captain Mahendra Singh Dhoni.
"Even after losing three games in a row, we just had a meeting of 50 seconds today. That shows how the franchise is , and that really connects with the person I am," Samson said.
Despite the win, Chennai are only ninth in the 10-team standings with two points from their four games. Delhi are fourth with four points after their second loss of the campaign.
In the early game on Saturday, Punjab Kings chased down Sunrisers Hyderabad's sizeable total of 219-6 in a high-scoring thriller to stay undefeated. Punjab have three wins from four, with one no result.