Powell hit four fours and five sixes in his unbeaten 68 from 36 balls and Pooran 62 that included five fours and three sixes from 42 balls in a partnership of 101 runs that ended midway the 19th over when Pooran was dismissed going for a bit hit with the West Indies still 27 runs from their target.
The pair came together after coming together with the score at 59-2 with Brandon King (22) and Kyle Mayers (9) back in the hutch after 8.3 overs.
Needing 25 from the last over, Powell gave the West Indies hope with consecutive sixes off Harshal Patel to leave the West Indies needing 11 from the final two deliveries. However, those deliveries yielded just two runs and the West Indies were short of their target.
The West Indies won the toss and sent India to bat. Their bowlers restricted India to 72-3 inside in the 10th over. Sheldon Cottrell dismissed Ishan Kishan for 2 before Roston Chase removed Rohit Sharma for 19, Suryakumar Yadav for eight and the dangerous Virat Kohli for 52 as India rushed to 106-4.
A 76-run partnership between Player of the Match Risbah Pant, 52 not out from 28 balls and Venkatesh Iyer (33) then powered India to their total of 186-5.
Chase finished with figures of 3-25 but the other bowlers let the West Indies down. Jason Holder conceded 45 from his four overs, including 14 from his last over, while Sheldon Cottrell who had only given up five runs from his first two overs, conceded 15 in his third and final over for figures of 1-20.
Pollard’s only over yielded 14 runs.
A delayed start to the contest meant it was limited to 16 overs per side, and KKR made it to 157-7 with Venkatesh Iyer producing a quick-hitting 42 runs from 21 balls, as Jasprit Bumrah (2-39) and Piyush Chawla (2-28) both made an impact with the ball.
While Sunil Narine went without scoring, Andre Russell contributed a 14-ball 24 toward the backend of the KKR innings, including two fours and two sixes.
The Indians looked likely to chase down their victory target when they reached 65-0 in the early stages, as they looked to improve on a fine 7-3 record at KKR's Eden Gardens.
But the wicket of Ishan Kishan in the seventh over sparked a rapid collapse, with Mumbai – already eliminated from the competition – quickly falling to 92-5 and ultimately losing by 18 runs.
Russell returned to grab 2-34 from three overs, sharing the wickets with Harshit Rana (2-34), Varun Chakaravarthy (2-17) and Narine, who had 1-21 from his three overs.
KKR remain top of the standings. As well as being the first team to seal their progress, they look good to secure a crucial top-two finish which would give them two chances to reach the final. They now have 18 points, two clear of Rajasthan Royals, who play Chennai Super Kings in one of two games due to take place on Sunday.
Data Debrief: Bumrah eyeing Purple Cap
While this was the latest setback in a highly disappointing season for Mumbai, who are second-bottom of the standings, Bumrah has been a prolific threat.
He took another two key wickets in this one, removing KKR dangerman Sunil Narine for a golden duck and halting a charge from Rinku Singh (20 from 12) in the final over.
That took India bowler Bumrah's season tally to 20, putting him level with Punjab Kings' Harshal Patel at the top of the Purple Cap standings.
The final figures could have been even better for Bumrah, who was frustrated to be hit for six by Ramandeep Singh (17 from 8) in the final ball of the KKR innings and earlier had an lbw decision against Nitish Rana (33) overturned on review.
However, a difficult period of form continued for Bumrah's team-mate Rohit Sharma in his team's unsuccessful run chase.
The opener came into the match with scores of 6, 8, 4, 11 and 4 in his last five innings and he was not much better here, struggling to 19 from 24 before falling to the superb Varun Chakaravarthy, who posted economical figures of 2-17 from four overs. That was quite the contrast to partner Kishan, who smashed 40 from 22.
