Kings XI racked up a total of 171 for four, with Shaun Marsh and David Miller hitting 45 and 44n.o. respectively.
Their swing bowlers did some early damage to Delhi who, despite a brave chase at the end, fell just short to slump to a 12th loss of the season.
Marsh’s 60-run opening stand with Adam Gilchrist (42) was a highlight for Kings XI’s batting performance.
Ben Rohrer did well for Delhi with 49 off 29 balls, but they couldn’t quite make it and stay second bottom of the IPL, ahead of Pune Warriors only on run rate.