The Royals posted 7-216 from their 20 overs led by makeshift opener Smith’s 69 from 47 balls which included four fours and four sixes, with CSK managing 6-200 in reply without ever really threatening the target.
The win is Rajasthan’s first from their first game of the 2020 Indian Premier League, while it leaves Chennai with a 1-1 record from two games.
Smith’s elevation was a big talking point, utilised at the top of the order in the absence of England wicketkeeper-batsman Jos Buttler who was unavailable after deciding to quarantine with his family.
“We will wait and see where I bat once Jos is available,” Smith said.
“I like to keep them guessing. On this wicket, it was all about trying to avoid straight hits for the spinners.
“A couple of balls were fuller and got above the eyeline but the idea was to stay back of a length.”
Smith’s 69 came alongside Player of the Match Sanju Samson’s knock of 74 from 32 deliveries, which included nine sixes, as they combined for a crucial 121-run second wicket stand.
Yashasvi Jaiswal, David Miller and Robin Uthappa all missed out with the bat for the Royals but Jofra Archer blasted 27 off eight balls at the death to set the high target.
Murali Vijay (21 from 21) and Shane Watson (33 from 21) couldn’t set any tempo in reply for CSK, while Faf du Plessis produced an excellent 72 from 37 balls to offer some hope.
The impressive Archer kept things tight with 1-26 from four overs while spinner Rahul Tewatia took three wickets to ensure the Super Kings were always at arm’s length.
CSK captain MS Dhoni said: “217 on the board, you have to had a very good start. That was not the case.”