Russell cracked an unbeaten 49 off 28 balls in Kolkata's formidable 6-177 total on Saturday and then took 3-22, including the key wicket of Kane Williamson off his second ball, as Hyderabad slumped to 8-123 and a fifth consecutive defeat.
Kolkata, who have lost Pat Cummins for the rest of the season after the Australian captain flew home with a hip injury, have kept alive their slim chances of reaching the playoffs.
Hyderabad need to win both their remaining games by huge margins and hope other results go in their favour to make the top four.
Kolkata made an impressive start in the batting powerplay as Ajinkya Rahane (28) and Nitish Rana (26) struck six sixes between them.
But India's new young fast bowling sensation, Umran Malik (3-33), removed Rana and Rahane in his first over immediately after the powerplay. Malik then had captain Shreyas Iyer caught in the deep in the next over.
Sam Billings combined in a 63-run stand with Russell, who batted deep.
The Jamaican smashed three of his four sixes in the last over off offspinner Washington Sundar, who ended up with 0-40. Russell hit him for 20 off the last six balls.
"Plan was to give Russell as much strike as possible and we were praying that he plays the last over because Washington had an over left," Shreyas said. "It worked out pretty well."
New Zealand captain Williamson's run of poor form continued for Hyderabad when he struggled for 17 deliveries before getting bowled by Russell on nine while attempting an extravagant shot while moving across his stumps.
Abhishek Sharma top-scored with 43 and Aiden Markram made 32 but the rest of the batters couldn't cope with the pace and spin of Varun Chakravarthy.
Fit-again Umesh Yadav bowled well in the powerplay and took 1-19, Tim Southee grabbed 2-23, and Russell returned and dismissed Sundar and Marco Jansen in the 18th over.
16°C