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The striker nodded home Craig Curran's cross and superb control allowed him to drill in a second.
Scott Boden's shot, touched by defender Andrew Davies, was allowed to stand despite referee Andrew Dallas whistling before the ball had gone in.
But Boyce replied with a towering header before a thumping shot from Ross Draper set up a frantic finale.
The hosts pressed for a leveller in the final 15 minutes, with Jake Mulraney and Liam Polworth going close with fierce strikes.
But County held on to pick up their first Premiership points, while Richie Foran's side are the only team yet to get off the mark after two matches.
With both teams exiting the League Cup and opening with league defeats last weekend, the game opened at a whirlwind pace.
Curran came into the County side to renew his often profitable partnership with Boyce and it paid off instantly.
An inch perfect cross found Boyce completely neglected by the home defence and the Northern Irishman took advantage with an accurate downward header from 10 yards.
Inverness were down to 10 men when the second goal arrived on 26 minutes.
Full-back Kevin McNaughton hobbled off with a knee injury and before his replacement, Lewis Horner, could get on, Boyce took Richard Foster's deep cross down with a sublime first touch before cutting past David Raven and smashing a low shot confidently into the corner.
County were well on top but the home team pulled one back in unusual circumstances shortly before half time.
Draper lofted a long ball over the top for Boden to chase and the striker squeezed a shot against the challenging Davies, with the ball spinning into the far corner.
Meanwhile, Dallas had blown his whistle and appeared to point to his assistant indicating a halt in play, only to immediately reverse that decision.
County players crowded the official, with goalkeeper Scott Fox saying he had been distracted by the whistle, although he did make a wholehearted dive.
Jim McIntyre's side put that behind them when Boyce completed his hat-trick early in the second half, rising at the back post to crash in a powerful header from a Christopher Routis free-kick.
Inverness gave themselves hope when Draper crashed a powerful low effort past Fox from the edge of the penalty area.
County then had to withstand a barrage of pressure as Erik Cikos headed off his own goal-line and Mulraney and Polworth went close.
Ross County manager Jim McIntyre: "Right from the off we were at it. Liam's second goal is fit to grace any league in the world.
"Today we put our chances away. You need to be good in both boxes to win football matches."
Goalkeeper Scott Fox: "The ball's in the box and just before Andrew Davies makes the block the whistle goes. I think he was saying it was offside. He made the wrong decision and admitted that to us which is a positive.
"I think I'm saving the shot as well I'm going a little more hard towards the ball. He's admitted he was wrong."
Inverness CT manager Ritchie Foran: "Defending. Poor defending. Switching off simple as that. We work hard on it as well. There's no excuses for it. I'll take my part of the blame they'll take their part.
"Boyce was the difference besides his goals his defending for Ross County was exceptional. He started them off, he was the difference.
"He's got hearts, desire, he's got hunger on and off the ball his work rate is immense. He bullied our boys today.
Overall we didn't deserve to win the game, we didn't even deserve to draw the game."
Match ends, Inverness CT 2, Ross County 3.
Second Half ends, Inverness CT 2, Ross County 3.
Attempt missed. Aaron Doran (Inverness CT) right footed shot from outside the box is high and wide to the left.
Substitution, Ross County. Jonathan Franks replaces Michael Gardyne.
Attempt saved. Aaron Doran (Inverness CT) right footed shot from the right side of the box is saved in the bottom right corner.
Substitution, Ross County. Ian McShane replaces Liam Boyce.
Attempt missed. Liam Polworth (Inverness CT) right footed shot from outside the box is high and wide to the left.
Substitution, Ross County. Alex Schalk replaces Craig Curran.
Foul by Liam Polworth (Inverness CT).
Michael Gardyne (Ross County) wins a free kick in the defensive half.
Christopher Routis (Ross County) is shown the yellow card.
Aaron Doran (Inverness CT) wins a free kick in the defensive half.
Foul by Christopher Routis (Ross County).
Jake Mulraney (Inverness CT) wins a free kick in the attacking half.
Michael Gardyne (Ross County) is shown the yellow card for a bad foul.
Foul by Michael Gardyne (Ross County).
Richard Foster (Ross County) is shown the yellow card for a bad foul.
Carl Tremarco (Inverness CT) wins a free kick on the right wing.
Foul by Richard Foster (Ross County).
Corner,  Ross County. Conceded by Gary Warren.
Attempt missed. Paul Quinn (Ross County) header from the centre of the box is too high.
Foul by Scott Boden (Inverness CT).
Paul Quinn (Ross County) wins a free kick in the attacking half.
Substitution, Inverness CT. Aaron Doran replaces Iain Vigurs.
Lewis Horner (Inverness CT) is shown the yellow card for a bad foul.
Andrew Davies (Ross County) is shown the yellow card for a bad foul.
Foul by Gary Warren (Inverness CT).
Craig Curran (Ross County) wins a free kick in the attacking half.
Liam Polworth (Inverness CT) wins a free kick in the attacking half.
Foul by Richard Foster (Ross County).
Ross Draper (Inverness CT) wins a free kick in the attacking half.
Foul by Andrew Davies (Ross County).
Attempt missed. Michael Gardyne (Ross County) right footed shot from outside the box is just a bit too high.
Corner,  Ross County. Conceded by Gary Warren.
Foul by David Raven (Inverness CT).
Craig Curran (Ross County) wins a free kick in the attacking half.
Attempt missed. Jake Mulraney (Inverness CT) right footed shot from the centre of the box is too high.
Corner,  Inverness CT. Conceded by Andrew Davies.
Attempt saved. Iain Vigurs (Inverness CT) right footed shot from the centre of the box is saved in the top left corner.
Corner,  Inverness CT. Conceded by Andrew Davies.
Liam Boyce scored a hat-trick as Ross County won an incident-packed derby with Inverness Caley Thistle.