Defender Lee Ashcroft gave the home side at Rugby Park a 16th-minute opener when the 20-year-old headed home his first goal of the season.
It was rich reward for a dominant first-half display from the home side but Inverness improved after the break.
But Scotland striker Boyd grabbed the clincher 16 minutes from time when the impressive Robbie Muirhead added an assist to a pair of near misses after twice hitting the woodwork in the first 45.
Killie now climb above St Mirren into eighth, but the defeat is another disappointment for recently-appointed Caley Thistle boss John Hughes after losing four of his first nine games in charge of the Highlanders.
The home side left new signing Vitalijs Maksimenko on the bench after his Friday switch from Brighton but did parade former playmaker Alexei Eremenko on the pitch at half-time as boss Johnston closed in on sealing the Finland international's return.
Inverness, meanwhile, had new assistant boss Russell Latapy viewing the action from the stand but the Trinidadian was left to watch helplessly as Caley Thistle struggled against a buoyant Killie side.
Muirhead thumped a low drive off the base of Dean Brill's left-hand post just 120 seconds in as the hosts made a sprightly start.
Rory McKenzie and Boyd then combined four minutes later but the former Rangers striker could not find a way past the keeper.
But it only took the Rugby Park side until just after the quarter-hour mark to finally break the deadlock as Sammy Clingan's prefect free-kick delivery was flicked home with the head by Ashcroft.
It took the visitors 10 minutes longer before they could seriously threaten for the first time as midfielder Liam Polworth drove into the Killie box before standing up a cross for Billy McKay, but the Northern Irishman saw his header sail just wide.
Kilmarnock, though, continued to look the more likely to score.
Thankfully for the Highlanders, the upright denied Muirhead for a second time after the 17-year-old connected with a fierce volley when Ashcroft miscontrolled another Clingan set-piece.
Caley Thistle looked a brighter outfit after the break but still could not find a leveller as Killie keeper Craig Samson stood up well to deny McKay after Ashcroft undercooked a back pass.
Inverness were forced into a change on 68 minutes as Josh Meekings and Muirhead were involved in a sickening head clash. The Killie man was able to return after some running repairs but Meekings had to go off clutching a nasty head wound while Daniel Devine went on in his place.
Hughes' side had undoubtedly improved since the interval but their lack of killer instinct invited a Kilmarnock sucker punch, which Boyd duly delivered with a quarter of an hour left.
With the Inverness defence backing off, Muirhead made the most of the space to slide a clever reverse pass into the 30-yard-old's path and he made no mistake with a finish high into the roof of Brill's net.
The strike took Boyd's tally for the season to 13 but he should have grabbed another seven minutes from time.
Instead, he inexplicably slotted 10 yards high and wide after McKenzie rolled in him for what should have been an easy finish.