Put in to bat first, five-time champions Chennai rode on Samson's unbeaten 101 off 54 balls to post 207-6 at Mumbai's Wankhede Stadium.
Chennai's West Indies spinner Akeal Hosein then returned impressive figures of 4-17 to bundle out Mumbai, who have also won the IPL five times, for 104 in 19 overs.
The colossal winning margin boosted Chennai's net run-rate and took them to fifth spot in the 10-team table. Mumbai slipped to eighth with five defeats from seven outings.
"They batted well," said Mumbai skipper Hardik Pandya. "It was the same track, it is the same soil. We should have just batted well."
Chennai started their innings briskly, courtesy of skipper Ruturaj Gaikwad's 14-ball 22 before he fell to Afghanistan spinner A.M. Ghazanfar in the third over.
Samson then teed off with three fours and one six off Pandya but kept losing partners at the other end, including Dewald Brevis for 21.
Undeterred, the 31-year-old took on the opposition attack, hitting 10 fours and six maximums across his well-crafted knock.
Samson, who was named player of the match, came into this edition of the IPL on the back of three half-centuries in the last three matches of India's T20 World Cup triumph on home soil in March.
"Feels great to score a century in Wankhede versus Mumbai," said Samson.
"After the powerplay, we kept losing wickets. I thought it's important for a settled batsman to bat through. The game tells you what to do."
Mumbai bowlers struck regular blows as Ghazanfar and left-arm quick Ashwani Kumar took two wickets each before Samson's final assault took Chennai past 200.
Samson reached his fifth hundred in the T20 tournament with a four on the final ball of the innings and raised his bat to acknowledge the applause from the fans and the dugout.
In reply, Mumbai lost three wickets, including South African Quinton de Kock for seven, in the first three overs and slipped to 11-3.
Impact substitute Hosein, a left-arm spinner, took two of the three.
Suryakumar Yadav, who made 35, and Tilak Varma attempted to rebuild in a partnership of 73 but the asking rate kept rising with some tidy bowling by Chennai.
The wily Hosein returned to break the stand as he got Varma to drag a delivery onto his stumps and out for 37.
Wickets kept tumbling as Noor Ahmad struck on successive balls to send back Pandya, for one, and Sherfane Rutherford for a duck, before Shardul Thakur avoided the hat-trick.
Hosein dismissed Suryakumar for his fourth wicket and, with that, the batting fizzled out.