Needing to win to stay afloat in the tournament, Kings XI made a wobbling start after they were being put into bat but made a late recovery to put up a respectable total at the PCA Stadium here.
From 63 for 3 at the halfway mark, Kings XI took 104 runs from the final 10 overs.
Kings XI lost wickets at regular intervals as they failed to stitch any big partnership. Their highest partnership was the 61 for the fourth wicket between Maxwell and Wriddhiman Saha (38).
Maxwell, Saha and Manan Vohra (25) got the starts but could not convert them to big scores.
Opener Vohra looked promising with a couple of fours off Sunil Narine at the start of the innings. He then hit two more boundaries off Umesh Yadav to up the ante.
But Yadav had the last laugh as he dismissed Vohra in the fifth over with his short delivery kissing the batsman's gloves for Robin Uthappa to do the rest behind the stumps.
Next over, Martin Guptill fell LBW to Narine as the batsman missed the delivery while trying to sweep over backward square leg and Kings XI were 41 for 2 then.
The home side were 42 for 2 after the powerplay overs and they were further in trouble as Shaun Marsh (11) departed after a promising start. The Australian played two delectable shots off Colin de Grandhomme, including a glorious straight drive, before he was out at Kings XI score of 56 for 3.
Marsh fell to a gem of a delivery off Chris Woakes. It was a full and straight delivery and Marsh played the line only to see it seam back in late to beat the inside edge before crashing into off stump.
Maxwell came out and he did not do much initially, scoring ones and two from his first nine balls he faced before taking his chances. He hit two consecutive sixes off de Grandhomme in the 12th over.
There was comparative lull for a couple of overs before Maxwell cut loose with two consecutive sixes off Kuldeep Yadav in the 16th over. But the same over, Maxwell was sent packing with Woakes taking a superb catch near the boundary running from long-off.