Green made an unbeaten 100 off 47 balls and put on a key partnership of 128 with skipper Rohit Sharma (56) as Mumbai achieved their victory target of 201 with two overs to spare at the Wankhede Stadium - their home ground.
Mumbai, five-time winners of the Indian Premier League, now await the result of the second match of the day between Royal Challengers Bangalore and holders Gujarat Titans to see if they can clinch the last remaining play-off spot.
The result eliminated the Rajasthan Royals from the play-off race while Bangalore, led by Faf du Plessis, remain in contention.
Bangalore need a win to make the next round, but a loss would allow Mumbai to go through.
Table-toppers Gujarat and second-placed Chennai Super Kings will clash in the first qualifier next week. Lucknow, who became the third team to book their play-off berth, await their opponent in the eliminator.
The winner of Qualifier One will head straight to the final in Ahmedabad on May 28th and the loser will play the winner of the eliminator.
Green, a big buy for Mumbai for $2.11million in the auction, stood out on Sunday with eight fours and eight sixes.
After Rohit's departure, Green kept up the charge and put on an unbeaten partnership with Suryakumar Yadav, who hit 25, to register their eighth win in 14 group matches.
Medium-pace bowler Akash Madhwal set up victory with figures of 4-37 to check Hyderabad to 200-5, a total that looked to go bigger but for some disciplined bowling.
Openers Mayank Agarwal (83) and Vivrant Sharma (69) put on 140 runs to lay the foundations for the total, which proved insufficient.
The departure of Sharma and then Agarwal made Hyderabad slide with the rest of the batting falling apart.
Hyderabad took the wooden spoon in the 10-team table.
