The opener dominated a low-scoring match, his 87 not out more than twice the next-best score as CSK won by eight wickets with 15 balls to spare.
Starc escaped fairy lightly, his 16 deliveries at Samson going for 14, including a wide with two fours. But more significant was he failed to dismiss the batter in his opening burst - because if you don't get Samson early, you are in trouble.
So far this IPL he has been dismissed for less than 12 runs six times in ten innings, but in the others he has made 115no, 101no, 48, and now 87no.
"I have been working a bit on my initial movement and it has been coming off," Samson said.
"I had to be a bit too selfish to get a hundred so I thought let's win the game ... finishing not out, winning the game gives you more satisfaction."
For almost everyone else the pitch looked difficult. Capitals made 7-155, a modest score by Indian Premier League standards. Sameer Rizvi (40no) and Tristan Stubbs (38) were the only players to pass 20 with spinners Akeal Hosein (1-19) and Noor Ahmad (2-22) exerting a stranglehold.
The home side had early hope when they dismissed Ruturaj Gaikwad (6) and Urvil Patel (17) to leave CSK 2-45 in the seventh and behind the rate.
Samson was then on 15, scoring at less than a run-a-ball, but ominously still there.
Kartik Sharma, 20 years old late last month, joined him and was the perfect foil. The pair gradually accelerated as they reeled in the target with a partnership of 114 off 66 balls.
Samson hit six sixes and Sharma, who finished with 41no off 31 balls to underline his evident promise, two.
Starc, who is still feeling his way back to match sharpness - this was his second outing since January after suffering shoulder and elbow injuries - ended with 0-30 off his four overs.
His team are now seventh, four points off the playoff pack with four matches to play. CSK have two points more.
