A mix-up between Dons defender Andrew Considine and goalkeeper Jason Brown in the fifth minute allowed Harkins to slide the ball in from close range.
Although the visitors responded positively, Dayton, on minutes earlier for Paul Heffernan, made sure of the points in the 65th minute when he beat Brown from the edge of the box.
It was another disappointing afternoon for Dons boss Craig Brown, who witnessed yet another lacklustre display while Kilmarnock boss Kenny Shiels watched his side move into the top half of the table without having to be particularly good.
The Irishman made two changes to his side with David Silva and Gary Fisher in for Danny Buijs, out with a hamstring injury, and Liam Kelly, who was suffering with a virus.
Brown dropped goalkeeper David Gonzalez to the bench, replacing him with his namesake Brown while Rory McArdle and Scott Vernon came in for Ryan Jack, out with a foot injury, and Josh Magennis who started on the bench.
Killie went into the game buoyed by last week's win over Rangers, their first at Rugby Park against the Light Blues in over 17 years.
The struggling Dons, one point ahead of bottom side Inverness at kick-off, were less confident and that showed when Harkins was gifted the opener.
A long punt by Killie defender Jamie Fowler looked aimless but with the swirling wind it had Dons defender Considine in trouble as he raced towards his own penalty area chased by the Rugby Park striker.
The Dons defender's headed pass-back was fumbled by Brown, allowing Harkins to collect the loose ball and slide into the net from close range, with Aberdeen stopper Youl Mawene making a vain attempt to block.
It was a needless error which instantly made it an uphill task for the visitors.
The rest of the half was scrappy to say the least, albeit the conditions did make it difficult for both sides to play football.
The Dons threatened little. In the 18th minute Vernon looked to be caught off-guard when Ricky Foster's cross from the left made it past Killie defender Mo Sissoko and the ball bounced off his head from six yards and was grasped by Kilmarnock goalkeeper Cammy Bell.
In the 34th minute, with nothing much ahead of him, Killie midfielder Dean Shiels sent in a curling shot from 25 yards but Brown gathered comfortably.
Three minutes from the break Aberdeen right-back McArdle caused Bell some alarm when he sent a cross from wide on the right just over the near post but it was more in error than judgement.
Brown started the second half for the Dons almost making a mess of a Mawene pass-back which did not augur well for Aberdeen, but they had Killie on the back foot moments later.
Midfielder Fraser Fyvie's curling free-kick missed everyone and skipped just past Bell's left-hand post seconds before the Killie keeper had to tip a McArdle drive from distance over the bar for a corner, but again the Pittodrie men could not take advantage.
As the crowd of 4,367 cowered in the stands from the swirling wind and rain the Dons remained on top without creating anything clear-cut.
Killie boss Shiels replaced striker Heffernan with Dayton in the 58th minute to try to get his side back into the game, before Magennis came on for Vernon minutes later.
However, the substitutions worked best for the home side who went further ahead after Harkins had sent Dayton racing clear.
The Killie substitute was pursued by Considine and as he slipped at the edge of the box he still got his low drive away which was powerful enough to beat Brown.
The visitors looked down and out and minutes later Foster was booked a for a cynical foul on Dayton as the home supporters cried for a more severe punishment.
The game petered out with not even a late rally from the Pittodrie men to give succour to their small but hardy band of fans who suffered yet another miserable afternoon.