En route to their third win in the cash-rich league, KKR chased a target of 150 with 10 balls to spare courtesy an unbeaten 51 off 44 balls (3x4, 3x6) from Bisla and a smashing 42 off 26 balls ( 3x4, 4x6) by Morgan. The duo blasted 72 runs in just over seven overs to pave the way for a smooth victory.
The win takes KKR to six points but they remain in seventh position in the league table.
Having been dropped after their shocking four-run loss to the same side in the first leg, it was a redemption time for Bisla, who also shared a crucial 66 runs with Jacques Kallis (37).
It was Manoj Tiwary's absence because of a split webbing paved the way for Bisla who showed glimpses of his last year's form in the final against Chennai Super Kings that had crowned them 2012 champions.
For the Kings XI Punjab's perspective, Mandeep dropping Bisla's catch when he had not even opened his account proved to be the big difference.
After being let down by Mandeep, Mahmood quickly turned the game around with two wickets from two balls when he bowled Gambhir and followed it up with an easy dismissal of an out-of-form Yusuf Pathan.
But for a change, the Knight Riders who were tottering at 10/2 showed some fine application with Bisla grabbing the opportunity in his comeback match.
Bisla took the challenge as he counter-attacked Mahmood when he stepped out to hit a six.
After returning with two wickets in first over, Mahmood conceded 12 runs in his second as the experienced Kallis too complemented well.
Bisla hit another six when he smashed Praveen over cover as the duo ensured a fine recovery stitching 66 runs for the third wicket.
Harmeet gave a crucial breakthrough taking the prized scalp of Kallis (37) but Bisla remained unfazed at the other end as he built another partnership when he along with Morgan took the match away from the Kings.
That little bit of luck also aided the hapless Knight Riders when a Chawla delivery to Morgan kissed the leg-stump without dislodging the bail as the ball raced to boundary.
It was then, Knight Riders took the attack on Kings with Morgan enthralling the crowd with his reverse sweeps and lofted drives, while Bisla rose up to the occasion showing fine application.
14 runs off Harmeet in the 13th over took equation in favour of the home side as they needed 49 in the remaining six overs with seven wickets in hand.
Kings XI Punjab had nothing going their way when Bhatt dropped a Morgan sitter at mid-wicket as Bisla went on to complete a deserving half-century.
Earlier, a quickfire 15-ball 28 not out by Gurkeerat Singh after the handy contributions from the middle order - Manan Vohra (31), Adam Gilchrist (27), Mandeep Singh (25) and David Hussey (21) - helped the team post the modest total.
On a day, when the KKR's spin ploy did not work, Kallis (4-0-14-2) with two crucial wickets in Mandeep and Hussey ensured that the home side did not let the Kings off the hook.
It was one of the rare day when Purple cap holder Sunil Narine went wicketless (4-0-22-0), while Sachithra Senanayake and legspinner Sarabjit Ladda conceded 47 runs from six overs together.
Balaji had to bear the brunt of Gurkeerat who hit the seamer for two sixes and one four in an 18-run last over that gave the Kings some rays of hope.
Opting to bat, Kings XI had a slow start with Senanayake beginning with a maiden against the struggling Kings skipper.
Mandeep however played freely at the other end hitting Balaji for two boundaries before charging out to Narine for the same effect to keep the scoreboard ticking.
Gilchrist soon got into the act when he took on Senanayake resulting in 12 runs as they were 45 for no loss at the end of powerplay before Kallis made his presence felt.