Defending 164 on a slow surface that remained under cover for three days, KKR speedsters Yadav (3/13) and Morkel (2/23) shared five wickets between them, while Piyush Chawla also bowled smartly to restrict Kings XI Punjab to 135/8 in 20 overs and hand KKR a record eighth victory on the trot.
Sent into bat, KKR had posted 163 for eight, riding on in-form opener Robin Uthappa's 30-ball 42.
Orange Cap holder Uthappa once again laid the foundation with the help of four boundaries and two sixes in his 10th consecutive 40-plus score, to push KKR's total in a rain-interrupted match.
With KXIP at 17/1 in 3.2 overs, drizzle had started to fall and they were well behind the Duckworth-Lewis equation of 37 required from five overs. The umpires, though, decided to continue with the proceedings.
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Manan Vohra smacked Shakib Al Hasan for two consecutive sixes in the next over to make the equation in KXIP's favour with the scoreboard reading 39/1 from five overs.
Dangerman Glenn Maxwell (6) did not last long and was trapped by Yadav and KXIP were 55 for three in 7.5 overs, 11 runs behind the par score.
It was Saha, who looked steady in the middle and kept KXIP in the hunt with some stunning strokes, but Morkel ensured that the wicketkeeper-batsman did not prolong his innings.
David Miller was dropped on 1 but he could not make it count and was castled by Piyush Chawla, while Yadav claimed his third victim in the form of the skipper George Bailiey.