Watson (104no from 59 balls) smoked Kolkata???s attack for nine fours and five sixes as the Royals posted 199-6, and Kolkata could only reply with??190-9 due to some stellar stellar bowling from Chris Morris (4-23).
Rajasthan are up to second in the table and can finish no lower than fourth, but reigning champions Kolkata now require an unlikely set of results in Sunday’s league-phase finale??to make the knockout stage.
Watson and opening partner Ajinkya Rahane (37 from 22) combined for a pulsating partnership of 80 before the latter was run out from the final ball of the seventh over at Brabourne Stadium.
Andre Russell (3-32) came to the fore for Kolkata in the middle overs, claiming the wickets of Royals captain Steve Smith (13), Sanju Samson (9) and James Faulkner (6) with his seam bowling.
But Watson continued his onslaught and completed his second IPL hundred ??? the other, a 58-ball 101, came against Chennai in 2013 ??? by creaming Umesh Yadav to the fence in the last over.
Gautam Gambhir (1) lasted just three balls of Kolkata???s??innings but the visitors kept up with the run rate thanks to some enormous blows from Yusuf Pathan (44 from 35) and Russell (37 from 20).
However, when??Morris accounted for Russell and Suryakumar Yadav (0) in the 14th over and Watson (2-38), who had been expensive with the ball, had Pathan pouched at the start of the 16th,??the Knight Riders??? charge faded.
Shakib Al Hasan (13 from 11) and Yadav (24no from 11) found the ropes to leave Kolkata requiring 16 from the last over but the impressive Morris returned to seal Rajasthan???s triumph.
Kolkata now need Sunrisers and Mumbai???s Sunday clash to be abandoned or for Bangalore to suffer an extremely heavy defeat to the already-eliminated Delhi Daredevils to make the last four.