Powered by David Warner's fighting 65-run knock and his stellar 111-run partnership with Lokesh Rahul (46), Hyderabad overcame a shaky start to score a competitive 172 for five after being invited to bat.
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After losing three quick wickets, Mumbai fought through big-hitting Kieron Pollard (78) and Ambati Rayudu (35 off 27) but all they could manage was 157 for seven in the end.
The defeat means that Mumbai Indians now need to win most of the nine matches in the Indian leg to make it to the knockout stage of the tournament.
Pollard prevented it from becoming a one-sided match with his scintillating 48-ball knock, embellished with six sixes and three fours.
Irfan Pathan bowled Pollard in the first ball of the final over, in which Mubai needed 20 runs. It was Pollard, who had brought Mumbai this far and his wicket at the crucial juncture dashed hopes of the defending champions.
Bhuvaneshwar Kumar also played a stellar role in Hyderabad's win as he gave away just 17 runs in his four overs and also took two wickets.
Led by a ferocious Dale Steyn, the SRH attack rocked the
Mumbai top order by taking three quick wickets. Bhuvaneshwar
was incredible in his two-over spell as he conceded just three runs and also got the rival skipper Rohit Sharma (1).
An intimidating Steyn had Corey Anderson (1) caught on a well-directed bouncer. Darren Sammy joined the party by castling opener Ben Dunk (20), reducing Mumbai to 31 for 3 inside powerplay overs.
Pollard and Rayudu brought some respectability to the Mumbai's chase with their fighting knocks. The tall West Indian hit spinner Amit Mishra for two sixes and a four in the 13th over and dispatched Karan Sharma for a humongous hit in the next over to raise hopes of a turnaround.
32 runs in those two overs made it a contest and Mumbai now required 74 runs in 36 balls. Dhawan brought Bhuvaneshwar back into the attack and the paceman continued his with good form, conceding just six runs from his third over.
Pathan broke the stand by dismissing Rayudu but there was no stopping Pollard, who again took Mishra (0/54) to cleaners by hitting him for three consecutive sixes and a four in the 17 over.
Earlier, Warner worked hard for runs initially but once he got his eye in and was settled, the Australian left-hander scored runs at a brisk pace. He hit more sixes (4) than fours (1) in his 51-ball knock before departing towards the end of the SRH innings.
Rahul also contributed in Hyderabad's decent total by supporting Warner well in their third-wicket stand, following cheap dismissal of their openers. Veteran paceman Zaheer Khan (2/26) bowled with good rhythm and succeeded in sending Shikhar Dhawan (6) and Aaron Finch (16) back to dugout inside the first five overs.
The SRH skipper edged one to Harbhajan Singh in slips immediately after hitting a boundary while Finch, who yet again looked in good touch, failed to keep a drive on the ground and was caught in covers by Ben Dunk.
Lasith Malinga and Harbhajan Singh also bowled well and at the same time SRH batsmen did not lack in application and were maintaining a decent run-rate. Prgyan Ojha was the only Mumbai bowler who failed to make an impact. He was hit for consecutive boundaries by Rahiul and was also punished by Warner, who smashed the spinner to a huge six over the mid-wicket.
In his first two overs, the left-arm spinner leaked 25 runs, allowing SRH to overcome the early loss of the openers. At half-way mark, SRH were 71 for two, albeit there were not much boundaries, only six at that stage. Warner and Rahul had to work hard for runs. They relied on rotating the strike, rather then going for big shots.
In fact, at one time, the gap between two boundaries was almost six overs. The shackles were broken when Ojha returned. He first fired his second wide for five runs and then Warner again hammered him for a massive six. Warner did not spare Pollard and even umpire Kumar Dharamasena, who was hit on his shoulders by one of his furious shots.