Ross Draper's free header from a 13th-minute set-piece sent Caleyon their way and, apart from one first-half chance for Leigh Griffiths, Hibs never looked like getting back in the game.
Caley Thistle stepped up a gear after a dull first half and Richie Foran and McKay secured their deserved win in the final 14 minutes as they stayed three points behind leaders Celtic.
But Fenlon's game plan was soon undone when Draper was afforded too much space to head home after Alan Maybury had fouled Andrew Shinnie 25 yards out.
Graeme Shinnie swung in the free-kick and Draper had several yards on Paul Hanlon to head into the corner of the net from near the penalty spot.
Inverness defended stoutly as Hibs tried to get into the game until a mistake in the 32nd minute allowed Griffiths the sort of chance he has been taking all season.
The on-loan Wolves striker was clean through after Josh Meekings failed to cut out a hopeful ball forward by Jorge Claros but Antonio Reguero acrobatically tipped over his attempt to lob the ball home.
Ben Williams was fully behind a curling 25-yard effort from Owain Tudur Jones and Draper soon provided a sterner test from similar range after some good passing and movement but the goalkeeper pushed away the powerful strike.
Inverness created the first chances after the break. Aaron Doran shot wide on the run from 20 yards after getting ahead of the home defence following a header on by Tudur Jones, who saw another powerful long-range strike saved.
Hibs very briefly threatened to stage a comeback with a short spell of pressure but Inverness went back up the park to put the game out of sight in the 76th minute.
Right-back David Raven crossed from near the corner flag and Foran threw himself in front of Alan Maybury to force the ball home from close range.
Hibs moved to a 4-3-3 when Shefki Kuqi replaced David Wotherspoon but they fell further behind with three minutes left.
McKay laid the ball off for young player of the month Doran and then ran into the box to meet the Irishman's inviting cross and head into the bottom corner from six yards to take his season's tally to 11 goals.