Middle-order batter Rinku is Kolkata's leading scorer this season with 337 runs from 11 matches, scoring them at a 151-plus strike rate.
The left-handed batter famously smashed five sixes in an over in their shock win against defending champions and league leaders Gujarat Titans last month.
Kolkata, chasing 180 against Punjab, needed 26 runs from 12 balls and Russell, who smashed 42 off 23 balls, hit Sam Curran for three sixes in the penultimate over to put his team on the brink of victory.
With the target reduced to six from six balls, Russell blocked the first ball from Arshdeep Singh and took a single off the next, showing how much faith he had in Rinku to finish the game.
Russell was eventually run out on the fifth ball but Rinku hit the final delivery for a four to keep Kolkata, currently fifth in the points table, alive in the playoff race.
"I get goosebumps seeing him doing what he's been doing," Russell said after collecting the Player of the Match award.
"I have company at the back end, he soaks the pressure off and he's been here for years now, a really hard-working guy."
The Jamaican later told reporters he would have refused a single and remained at the striker's end had it been any other player.
"He's just a fearless player. Wherever you bowl, he has a shot to counter that delivery," Russell said of Rinku.
"I gave him a hug and said, 'Listen, bring home the bacon for us ... we need you at this point'. He said 'Okay big man, no worries.'"
Two-time winners Kolkata host 2008 champions Rajasthan Royals in their next match on Thursday.
