After two back-to-back wins, Kings XI Punjab will play against Gujarat Lions at Mohali.
Narine smashed four boundaries in a quick 18 before he was bowled by Mohit Sharma.
20 runs were needed off the last over of the match and Sandeep gave away just 5 runs off it as Punjab kept their hopes of a play-off berth alive with this thrilling win.
Sunil Narine (18) was first to fall with Knight Riders 39 runs into their chase, while Lynn stood firm to rack up 84 from 52 deliveries opposite a rotating cast of disappointing batting partners.
The middle order of KKR is led by Manish Pandey - 345 runs in 12 matches - as he holds the match together before Yusuf Pathan can come and launch the onslaught whenever required. Captain Gautam Gambhir scored just 8 runs.
They achieved the target with 29 balls to spare on the back of Sunil Narine's (54 off 17 balls) record joint fastest IPL 50 - from 15 balls - and an equally aggressive knock from Chris Lynn (50 off 22 balls).
KKR were 82 for 3 at the halfway stage, needing another 89 to win the match.
That left Lynn in the spotlight and the Australian didn't disappoint, easily dispatching a Matt Henry over the rope and continuing to find the boundary regularly, despite failures from Gautam Gambhir (eight) and Uthappa, superbly caught by Axar Patel off Tewaita's next ball for a duck.
Put in to bat, Punjab did not have the best of starts but they had a course-correction of sorts, thanks to a steady 38 from Wriddhiman Saha and an explosive 44 from captain Glenn Maxwell which took them 167/6.
After that, it took the combined effort of Kings XI Punjab spinners-Axar Patel and Rahul Tewatia-to stem the flow of runs.
Having won two games in a row, both in impressive fashion, Kings XI's momentum came to a halt on Sunday, when the Gujarat Lions chased down a score of 189 to hand the home side a frustrating loss in Mohali.
He was assisted for a large portion of his innings by Shaun Marsh (58 off 43 balls) after losing opening partner Martin Guptill (2) early on.
Narine got his ticket to open the KKR innings after Chris Lynn suffered an injury in their second match of the IPL against Mumbai Indians and what a revelation he been since - 196 runs in 12 runs. What makes things even more hard for KXIP is that their remaining two matches after this one are against Mumbai Indians and Rising Pune Supergiant, both teams that look in ominous form and are among the top three in the League at the moment.
Yadav though had the last laugh as he dismissed Vohra in the fifth over with a short delivery.
The hosts were further in trouble as Shaun Marsh (11) departed after a promising start.