Chasing a target of 152, India opener Samson was imperious as he smashed seven fours and six sixes as his knock came off just 52 deliveries.
Proteas seamer Lungi Ngidi, returning from injury, dismissed visiting skipper Ruturaj Gaikwad (6) while Urvil Patel (17) fell to the spin of Axar Patel as Chennai slipped to 45-2 in the run-chase.
Samson though received good support Kartik Sharma, who scored a 31-ball 41 as the Super Kings got over the line with more than two overs to spare.
The Capitals had earlier stumbled their way to a total of 155-7 in their 20 overs, which was never going to be enough on a good surface at the Arun Jaitley Stadium.
The home team found themselves in deep trouble at 69-5 after 11 overs before Proteas batter Tristan Stubbs and Sameer Rizvi tried to save the situation.
Stubbs made his way to 38 from 31 balls while Rizvi was unbeaten on 40 off 24 deliveries as the Capitals went over the 150-run mark that proved to be unfruitful.
Ryan Rickelton and Rohit Sharma produced a stunning opening stand to steer Mumbai Indians to a commanding six-wicket win over Lucknow Super Giants on Monday, keeping their faint IPL playoff hopes alive with a record chase at the Wankhede Stadium.
Kolkata Knight Riders kept their IPL playoff hopes alive with a seven-wicket win over Sunrisers Hyderabad as the Gujarat Titans claimed a vital four-wicket win over table-toppers Punjab Kings.
Chennai Super Kings kept their Indian Premier League 2026 campaign alive with a commanding eight-wicket victory over Mumbai Indians, a result that simultaneously ended their rivals' hopes of reaching the playoffs.
Delhi Capitals produced a record-breaking chase to defeat Rajasthan Royals by seven wickets in a high-scoring Indian Premier League clash at the Sawai Mansingh Stadium in Jaipur on Friday.
