Dougie Imrie had put the visitors ahead inside 15 minutes and Garry Wood doubled their advantage just before the interval by taking advantage of an error by Kilmarnock goalkeeper Alan Combe.
Home substitute Willie Gibson threw Kilmarnock a lifeline with his strike six minutes from time but Taouil's miss cost his side a point.
Inverness won the game's first corner after three minutes but as the players jostled to receive Imrie's ball from the right, Black clattered heavily into home goalkeeper Combe on the six-yard line.
Combe carried on after some extended treatment but in the meantime Black had become an early entry into the book on the advice of the assistant referee.
Wood then had two pacy excursions into the penalty area but the second produced only a yellow card for diving as he failed to find a way through.
Inverness went in front after 13 minutes when defender Garry Hay failed to deal with Cowie's ball across the face of goal, allowing it to run behind him to Imrie, who controlled and fired in a first-time shot from an acute angle off the underside of the crossbar.
Kilmarnock failed to trouble visiting goalkeeper Ryan Esson throughout the opening half-hour and instead it was the visitors who doubled their lead in calamitous fashion for Kilmarnock.
Cowie's corner from the left was headed back out to the flank by Manuel Pascali but the Inverness player swiftly volleyed it back in and Combe spilled it on his line, giving Wood a simple task of nodding home.
Kilmarnock rallied as the first half entered five minutes of stoppage time but David Fernandez's shot from the edge of the area was easily saved.
Taouil inspired their best forward forays and he came close with a cross from the left which saw Allan Russell just unable to connect with a header right in front of goal.
Combe was replaced at
half-time by Frenchman Damien Rascle and an already fiery game continued to overheat in the second half with a series of crunching challenges from both sides, most notably on Fernandez on the halfway line, and a flurry of yellow cards from referee Stephen Finnie.
Taouil weaved into the left of the box cut back for Russell but his header was cleared and the Moroccan then curled in a 25-yard free-kick which went just over.
Rascle made his first save just after the hour, clawing the ball to safety as Wood attempted to prod home on the goalline after a quick break upfield.
Esson matched that with three impressive saves in quick succession as Kilmarnock enjoyed their best attacking spell as the game entered its final quarter.
The Inverness goalkeeper reacted well to punch off the line from Fernandez's powerful header, cleared the subsequent corner and when it was volleyed back in from the edge of the box, palmed over.
Kilmarnock dominated the final half-hour but saw James Fowler miss a golden opportunity to reduce the deficit when Fernandez fired an inviting cross from the left all the way across goal only for the defender to fail to connect.
Substitute Andrew Barrowman was caught offside when Inverness put the ball in the net from a rare forward foray and at the other end Gibson came close with a diagonal effort 10 minutes from time.
The Kilmarnock substitute succeeded in reducing the deficit six minutes from time, cutting in from the left and playing a one-two with Fernandez before firing home a low drive.
It set up a grandstand finish and when Ross Tokeley brought down Gibson Taouil stepped up to take the penalty but blazed over, with Fernandez also heading over in injury time.