Put in to bat, Mumbai started slowly before Sarfaraz Khan and Sujit Nayak batted aggressively to guide the team to a challenging total of 145 for five.
The duo, both of who remained unconquered, piled on 46 runs in just 16 balls for the sixth wicket.
Sarfaraz, who made his T20 debut, made a breezy 20-ball 36 that included four fours and a six while Nayak played a blinder, scoring 23 runs off seven balls with tbe help of two fours and as many sixes.
Saurashtra started the run chase slowly and scored just 19 runs in the first six over. They couldn't accelerate their innings and fell short of the target at 129 for seven.
More From This Section
Cheteshwar Pujara opened the innings to make a 60-ball 62 and stuck seven fours and a straight field six off left-arm spiner Nayak.
The India Test no. 3 played a lone hand to remain unbeaten till the penultimate over while Sheldon Jackson made 26 and skipper Jaydev Shah notched up 14.
Left arm Zaheer got rid off Pruthvi Solanki in the next ball and would have got another wicket in the same over but for a dropped catch. Medium-pacer Prathamesh Dhake scalped three wickets, while Zaheer bagged two.
This was Saurashtra's second successive loss and Mumbai's second win in three games.
Brief scores: Mumbai 145 for 5 (Sarfaraz Khan 36, Aditya Tare 29, Sushant Marathe 25; Arpit Vasavada 4 for 19, Jaydev Unadkat 1 for 37) beat Saurashtra 129 for 5 (Cheteshwar Pujara 62, Sheldon Jackson 22; P Dhake 3 for 25, Zaheer Khan 2 for 29.