By virtue of this win, Rajasthan have now moved to the sixth position in the eight-team standings with 10 points from 12 games. On the other hand, despite the loss, Sunrisers have just managed to hold to their fourth place in the table with 10 points from 11 games.
Opting to bowl in a must-win match, Rajasthan first restricted Sunrisers to 160 for eight and then chased down the target in 19.1 overs.
In reply, Liam Livingstone (44 off 26) and Ajinkya Rahane (39 off 34) got Rajasthan off to a flying start with the former taking the attack to the opposition. The duo raced off to 78 off 55 balls for the opening wicket, picking up 60 runs off the first six powerplay overs before Livingstone perished.
An over later Rajasthan suffered yet another blow in the form of Rahane, caught by David Warner at long-off off Shakib Al Hasan (1/26). Then Sanju Samson (48 not out off 32) and skipper Steve Smith (22) held fort and shared 55 runs in 5.3 overs to take Rajasthan within sniffing distance of win before the latter departed.
Earlier, Manish Pandey hit a quick half-century before Sunrisers witnessed a middle-order collapse to be restricted to 160 for eight.
Sent into bat, Sunrisers got off too a good start even after the early dismissal of skipper Kane Williamson (13) with Warner and Manish Pandey sharing 75 runs off just 50 balls for the second wicket before losing the plot after the halfway stage.
Pandey reached his fifty in 27 balls with the help of eight fours but just when the partnership was looking threatening, a brilliant catch by Smith sent Warner packing.
Warner backed away a long way and tried to slap an Oshane Thomas (2/28) short delivery over extra cover but didn't time the shot perfectly and Smith ran back and dived full length to his right to hold on to a beautiful catch.
Pandey continued his aggressive instinct and lofted Gopal over extra cover for an exquisite boundary. But the leg-spinner hand the last laugh as he dismissed Pandey in the very next ball, brilliantly caught by Samson as Sunrsiers slumped to 121 for three after 15 overs.