Harbhajan Singh also did some damage with 2-23, including the important wicket of Warner, who had smashed seven fours and two sixes. In reply, Parthiv's quickfire knock along with Nitish Rana's 45 and Krunal Pandya's 20-ball 37 helped the hosts reach the target with eight balls to spare.
In the bowling department, all eyes will be on the 18-year-old Afghani, who already has five wickets from two outings.
The Mumbai Indians will look to assert their dominance at home when the Sunrisers Hyderabad land up at the Wankhede Stadium for an IPL 2017 match on Wednesday.
To add to their woes was some brilliant bowling by Jasprit Bumrah in the death overs as he finished with figures of 3 for 24 from his quota, bowling two in the Powerplay and two in the death, to restrict the visitors to a sub-par 158 for 8 on a batting paradise.
Batting first, Sunrisers were given a rollicking start by David Warner (49) and Shikhar Dhawan (48).
The match also saw Sunrisers star Mustafizur Rahman bowl his most expensive over in T20 cricket.
Parthiv Patel put the two-time champions on course for victory after Jos Buttler and Rohit Sharma failed, the latter totally foxed by a googly from Afghanistan spin sensation Rashid - who took 1-19 from four excellent overs. Warner's return to form will also keep Mumbai anxious.
In the very next over, he got a huge slice of luck as a Krunal Pandya catch was ruled by the umpire as not out, with replays not clearly suggesting whether the ball hit the ground as Pandya tumbled to the ground after taking the catch at mid-off.
Hyderabad next face the Knight Riders on Saturday while Mumbai Indians take on the winless Lions the following day.
The Englishman has looked good at the top in both the matches and has forged a good partnership with Parthiv Patel. With him fit and available for the selection, Warner will cast out his options to play Mustafizur in today's game in place of Cutting.
5 Number of matches after which Sunrisers Hyderabad lost an IPL match. Dhawan scored just 48 runs off the 43 balls he faced, and his dot balls were a regular feature of his innings. Pacers Ashish Nehra, Bhuvneshwar Kumar and Henriques have complimented each other well and will surely test the Mumbai batsmen.