Narine's blitz, laced with six fours and seven sixes, guided Kolkata to 235-6 after they were invited to bat first in Lucknow's final home game.
Two-time champions Kolkata bowled out Lucknow for 137 in 16.1 overs for their eighth win in 11 matches and almost guaranteed a play-off berth. Second-placed Rajasthan Royals have played one match fewer.
In the first game of the day, all-rounder Ravindra Jadeja starred with bat and ball to help holders Chennai Super Kings climb to third with a 28-run win over Punjab Kings.
The top four teams will make the play-offs with the final on May 26 in Chennai.
Narine, who has impressed after being promoted to open by Kolkata this season, led their batting charge in a 61-run first-wicket stand with Phil Salt.
"He was splendid," Kolkata skipper Shreyas Iyer said of his team's player of the match Narine, who has amassed 461 runs at a strike-rate of 183.66.
"The start from openers has been great. Pure bliss. We just want to keep continuing the momentum so that we get to the great total and be optimistic."
Lucknow's Naveen-ul-Haq took three wickets to hurt KKR but Iyer, who made 23, and Ramandeep Singh, who hit a six-ball 25 not out, helped the team finish on a high.
Ramandeep returned to make an impact in the field as he took a stunning catch to dismiss Arshin Kulkarni when he ran back 21 metres to dive and pouch the ball off the bowling of Mitchell Starc.
Marcus Stoinis hit 36 but the rest of the batting fell flat as spinner Varun Chakravarthy and fast bowler Harshit Rana took three wickets each.
Andre Russell took two wickets and Narine returned figures of 1-22.
Pathirana blow for Chennai
Lucknow are fifth on the table and stay in the hunt for a play-off spot.
"Once we go back to dressing room, we move on from this game and see where we went wrong," said skipper KL Rahul. "Last home game, we are on the road for the next few games, we need to be little bit more fearless."
In the earlier match, Jadeja top-scored with 43 off 26 balls to guide Chennai to 167-9 batting first in Punjab's adopted home ground of Dharamsala.
Jadeja then returned figures of 3-20 from his four overs of left-arm spin to help restrict Punjab to 139-9 for Chennai's sixth win in 11 matches.
The performance from the veteran Jadeja comes as a welcome sign for India ahead of the T20 World Cup in June in the West Indies and the United States.
Chennai suffered an early blow with Sri Lanka pace bowler Matheesha Pathirana set to return home due to a hamstring injury.
Pathirana was Chennai's standout bowler and took 13 wickets in six matches.
But medium-pace bowler Tushar Deshpande took on the responsiblity in the absence of Pathirana and injured Deepak Chahar as he struck twice in his first over and Punjab's second in the chase.
Deshpande sent Jonny Bairstow, bowled for seven, and then Rilee Rossouw, bowled for a duck, trudging back to the pavilion in the space of four balls and the chase could never take off.
