Gambhir gunned down the opposition attack with a blazing inning, helping his team overcome the 171-run target in 16.3 overs.
The move to send Sunil Narine (37 off 18 balls) at the top of the order alongside Gambhir worked brilliantly as they smashed 76 off 34 balls to set up a comprehensive victory.
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The win for KKR came after a painful loss against Mumbai Indians and they now have two victories from three games.
It was the first loss of the season for Kings XI Punjab after two emphatic wins.
The game was very much in the bag for KKR with the flying start they got through Narine, who entertained the Eden crowd by slamming three sixes and four boundaries.
It was also a record-equalling 33rd IPL fifty for Gambhir who now shares the feat with David Warner.
The result proved that KKR are a tough side to beat at home and with today's win, they completed an 11th successful chase on this ground.
Earlier, India pacer Umesh Yadav made a successful comeback as his four wickets helped Kolkata Knight Riders restrict Kings XI Punjab to 170/9.
Yadav, who missed two matches because of a niggle following a hectic Test series against Australia, struck thrice in his fourth over to cover up for another poor display on the field.
KXIP were 95/2 after 10 overs before Umesh dismissed opposition skipper Glenn Maxwell (25 off 14) for his first wicket.
The visitors once again stepped up the momentum with Wriddhiman Saha (25 off 17) and David Miller (28 off 19) putting up 57 runs in 32 balls to put their team on course for a total close to 200.
KXIP were going comfortably at 145/4 in 17 overs when Umesh made his presence felt with a flurry of wickets to dismiss Miller and Saha, while Axar Patel (0) became his fourth victim.
Put in, Kings XI Punjab were off to a spectacular start with 10 runs from first over as Manan Vohra (28) and Hashim Amla (25) put on their second successive fifty-plus opening partnership.
Making full use of his reprieve on 17, Vohra took charge on the KKR opening pace duo of Umesh and Trent Boult.
The visitors were 47 for no loss after four overs and were in no mood to relent when Piyush Chawla broke the opening stand when Vohra was bowled after failing to read one that went straight off the re-laid pitch.
Chawla conceded just four runs in the last over of Powerplay as KKR went on to arrest KXIP's run flow with 14 runs from three overs.
The momentum temporarily shifted in favour of KKR who got a second breakthrough when Marcus Stoinis bottom-edged one to his stumps off Narine.
But poor catching once again hurt their cause and this time part-time wicketkeeper Robin Uthappa failed to take a regulation catch off Maxwell on five.
The miss proved costly as Maxwell hammered Chawla for 6 -4-4 in his next over that yielded 17 runs with 15 off them coming from the Aussie's blade.
Earlier Bollywood actress Shraddha Kapoor danced to Bollywood numbers in a 19-minute opening ceremony to mark the start of the first match of the season at Eden Gardens.
The show was a fusion of Bollywood numbers and traditional chhau dance as both the team captains, Gambhir and Maxwell, took the fair play pledge before taking the field.
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