The Royals, who won the toss and elected to field, restricted the visitors to 134-9 in their 20 overs as the Australian native took the 13th IPL hat-trick in history and the second of 2014.
However, Watson made just 11 with the bat as Rajasthan were dismissed for 102 in 19.5 overs at the Sardar Patel Stadium.
Watson clean-bowled his opposite number Shikhar Dhawan for 33 with the last ball of the fourth over and then returned in the 17th over to have Moises Henriques caught at long-on and Karn Sharma caught behind in consecutive balls.
Sunrisers' lower order struggled with Amit Mishra involved in a comical run out at the third attempt.
Irfan Pathan, with an unbeaten run-a-ball 21, was the only batsman outside the top four to make it into double figures.
|Sunrisers Hyderabad: 134-9 (20 Overs)|
|Shikhar Dhawan||b Shane Watson||33||20||165.00||7||0|
|Aaron Finch||c Ajinkya Rahane b Rajat Bhatia||9||10||90.00||1||0|
|Lokesh Rahul||b Rajat Bhatia||18||18||100.00||2||0|
|Naman Ojha||b Rajat Bhatia||17||19||89.47||1||0|
|David Warner||st Sanju Samson b Pravin Tambe||6||7||85.71||0||0|
|Moises Henriques||c Ajinkya Rahane b Shane Watson||9||13||69.23||1||0|
|Irfan Pathan||NOT OUT||21||21||100.00||2||0|
|Karan Sharma||c Sanju Samson b Shane Watson||0||1||0.00||0||0|
|Dale Steyn||run out (Sanju Samson)||9||8||112.50||1||0|
|Amit Mishra||run out (Sanju Samson)||0||2||0.00||0||0|
|Bhuvneshwar Kumar||NOT OUT||0||1||0.00||0||0|
|EXTRAS||(w 2, b 5, lb 5)||12|
However, their total soon looked a competitive one, as the hosts stuttered to 37-3 in the powerplay and then lost Watson in the first over after the lifting of the fielding restrictions.
A 37-run partnership between Stuart Binny and Steven Smith gave Rajasthan hope, but the latter was superbly run out by David Warner for 12, and the Australian became Dale Steyn’s second victim after making 22.
Bhuvneshwar Kumar dismissed James Faulkner, Rajat Bhatia and Kane Richardson in the 18th over to finish with 4-14 before Pathan sealed the victory with the penultimate delivery of the match.
|Rajasthan Royals: 102 (19.5 Overs)|
|Ajinkya Rahane||c David Warner b Bhuvneshwar Kumar||0||3||0.00||0||0|
|Karun Nair||c Naman Ojha b Dale Steyn||12||9||133.33||3||0|
|Sanju Samson||b Karan Sharma||16||16||100.00||1||1|
|Shane Watson||c Naman Ojha b Moises Henriques||11||10||110.00||1||0|
|Stuart Binny||run out (David Warner)||12||19||63.15||0||0|
|Steve Smith||c Irfan Pathan b Dale Steyn||22||33||66.66||0||0|
|Rajat Bhatia||c David Warner b Bhuvneshwar Kumar||4||8||50.00||0||0|
|James Faulkner||c Aaron Finch b Bhuvneshwar Kumar||4||6||66.66||0||0|
|Kane Richardson||c & b Bhuvneshwar Kumar||1||2||50.00||0||0|
|Dhawal Kulkarni||NOT OUT||7||6||116.66||1||0|
|Pravin Tambe||c Dale Steyn b Irfan Pathan||3||7||42.85||0||0|
|EXTRAS||(w 5, b 4, lb 1)||10|
Rajasthan remain in third place in the standings after their third loss in eight games, while Hyderabad picked up their third victory and could even up their win-loss record by beating Delhi Daredevils on Saturday.