The pair got off to a strong start and eventually reached a combined 60 runs before Singh was taken out after hitting 21 from 15 deliveries.
Sehwag (30) was the second to go, but it was David Miller who finished top scorer in Punjab's innings by securing a knock of 66, which included eight boundaries.
Gayle, who has admitted that he is still struggling with injury, could only muster four runs from seven balls, while his replacement Virat Kholi was sent packing for a duck following a Sandeep Sharma delivery.
Sharma took three wickets during the innings to halt Bangalore's attack, but AB de Villiers tried to respond by scoring 53 before getting dismissed.
Bangalore could not match the required run rate in the final overs, needing 50 off the final six balls, but managed 18 to give Kings XI their seventh win of the season.