Archer's fantastic cameo gave Royals a huge total to defend against the Super Kings.
After a middle-order collapse following the dismissal of in-form Samson, RR looked like settling for a score around 180-190 in flat batting conditions on a ground with small boundary dimensions.
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But Archer's crucial blitz in the slog-overs allowed them to sail past the 200-run mark, with little help from CSK's Lungi Ngidi, who really struggled for control at the death.
Archer punished each of Ngidi's mistakes and struck four sixes in his 8-ball 27* to take RR to an intimidating total of 216/7 which, despite the conditions, they were able to defend by 16 runs at the end.
In the second half also, England's Barbados-born speedster contributed with an incisive spell of 1/26.
"Jofra at the end was magnificent, getting us up to that total and then the boys did a good job with the ball... He came in and played an incredible inning tonight. He is a terrific player for us and did well with the ball as well," said Smith in the post-match press conference, as quoted by ANI.
In another matter, Smith said it won't at all be an issue fitting in Jos Buttler into a winning combination for the next match against Kings XI Punjab (KXIP) on Sunday (September 27).
Buttler has been in isolation since arrival to UAE because of COVID-19 regulations. The skipper, who opened in Buttler's absence on the day, said it will only bolster the side to have the explosive Englishman back at the top of the order.
"No, I do not think so, it gives us options. Jos coming back in the next match is a big plus for us," Smith said.