Rahane shared a 77-run fourth wicket partnership with Stuart Binny (48 not out) to rescue Rajasthan after they were precariously placed at 31-3 in 6.2 overs.
The 25-year-old Mumbaikar hit six boundaries in his 53-ball 59-run innings to anchor the chase as Rajasthan overhauled Hyderabad's score of 133-6 with three balls to spare at the Sheikh Zayed Stadium.
Earlier, Rajat Bhatia (2/22), Dhawal Kulkarni (2/23), Kane Richardson (2/25) and Pravin Tambe (0/23) bowled brilliantly as Rajasthan restricted Hyderabad to 133 for 6 in their stipulated 20 overs.
While Dale Steyn (2/29) trapped opener Nayar infront of his wicket only in his third ball, Samson was sent packing by Bhuvneshwar Kumar (1/21) when the batsman's miscued shot was caught by Dhawan in the fourth over as Rajasthan could only score 30 in their powerplay overs.
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In the next over, Ishant Sharma (1/29) had Watson caught behind by wicket-keeper Lokesh Rahul with an away going delivery as Rajasthan slumped to 31 for three.
Opener Ajinkya Rahane, however, dug his heels and started to weave a partnership with newman Binny.
The duo played sensible cricket as they kept taking ones and twos, besides the odd boundaries, to keep the scoreboard ticking. They brought up their 50-run partnership off 40 balls for the fourth Wicket.
Looking for a wicket, Dhawan brought Steyn back into the attack but his first ball went to the boundary as Rahane brought up his hard-earned fifty off 46 balls. The 25-year-old then dispatched the next ball for another boundary.