Ospreys, who have now lost five out of six matches, had rallied from 16-0 down at the beginning of the second half with converted tries for number eight Morgan and wing Hanno Dirksen in torrential rain at Swansea.
But Kings had done enough in the first half with a try for centre Erich Cronje and 11 points from the boot of full-back Scott Van Breda.
Ospreys’ poor form was not helped with nine players out injured, while a further eight are on an extended rest following the World Cup.
But the region was boosted with new signing Shaun Venter returning to the starting line-up.
The quality of the rugby by both sides was pretty poor in the opening exchanges not helped by persistent rain.
But Kings were the better side throughout the first half and deserved their 13-0 interval lead.
However, the Ospreys had been offside, and Van Breda made no mistake with the resulting penalty.
And it got better from the restart when fly-half John Jackson caught the ball and delicately chipped ahead for scrum-half Josh Allderman. Left wing Josiah Twum-Boafo and skipper Howard Mnisi combined before sending centre Cronje sprinting away over the line. Van Breda added the conversion.
Ospreys were caught offside on halfway at the end of the first half and Van Breda produced a fine 50-metre kick to convert the penalty – the last action of the half.
The poor quality of Ospreys’ first half was reflected by a change at the interval which saw Hook replace Luke Price.
But despite Hook’s involvement Kings increased their lead to 16-0 with a penalty in front of the posts.
Hook’s experience helped Ospreys upfield and after the forwards banged on the door for long enough number eight Morris dived over at the side of a ruck for the try. Hook converted.
Hook suffered an accidental knee to the head and was replaced temporarily by Price while Kings had Cronje sin-binned for persistent offending.
After a series of scrum resets which frustrated the crowd Ospreys got over the second time with Dirksen scoring with Price converting to cut the scoreline to 16-14.
But they were unable to convert two late penalty chances for Hook, who returned to the action – one from 30 metres and one from just inside the Ospreys half.
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