CSK won by 8 runs
Veterans MS Dhoni (75 off 46) and Imran Tahir (2 for 23) starred for their side as Chennai Super Kings completed their third consecutive victory of the Indian Premier League 2019.
With 176 to win for the Rajasthan Royals, the away team lost Ajinkya Rahane, Sanju Samson and Jos Buttler inside first four overs.
Steve Smith and Rahul Tripathi then shared a 61-run partnership to settle things down for their side.
However, the veteran leg-spinner Imran Tahir turned things around for CSK, removing Tripathi and Steve Smith to halt the run-chase for Royals.
With 56 required off 24 balls, Shardul Thakur struck immediately, getting rid of Gowtham (9 off 8 balls).
Stokes and Archer took on Dwayne Bravo, smashing 19 off his over to reduce the equation to 25 off 12.
The duo then managed to get 13 from the next over but Dwayne Bravo held his nerve at the end to restrict Rajasthan Royals to 167.
Earlier, CSK were in deep trouble when they lost Watson, Rayudu and Jadhav inside first five overs.
MS Dhoni and Raina then joined hands to pull their side out of trouble before Bravo chipped in with 27 off 16 balls.
Dhoni switched gears at the right time as CSK hammered 60 off the last three overs.
Chennai Super Kings now stand at the top of table with three wins.
MS Dhoni was declared man of the match for his superb batting performance.
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