McCourt had been been likened to Lionel Messi by captain Aaron Hughes in the build-up to this match and produced two goals the Barcelona ace would be proud of as Nigel Worthington's side reignited their Group C campaign in some style.
Hughes got the ball rolling after five minutes with his first international goal after 77 caps, before Steven Davis powered home a second from 25 yards.
But this was a night that will be remembered for a scintillating showing from Celtic's McCourt - remarkably starting his first competitive fixture at the age of 27.
With no goals in their two previous home qualifiers, an early breakthrough was necessary to ease some of the tension and Hughes obliged from the first corner of the match.
Sammy Clingan's delivery found Gareth McAuley at the far post and the defender was able to hook the ball across the six-yard box at full stretch.
Hughes was first to react and poked it over the line via the the post.
The Faroes' first attack came in the 12th minute through Christian Holst, who scored when the sides drew in the reverse fixture in Toftir, but Hughes was on hand to shepherd him away from the danger area.
McCourt, looking lively in possession, created a half-chance for David Healy after 15 minutes, but the Rangers man could only force a corner.
A slightly scrappy period began to unfold, with the Faroes still trying to find their feet in the game and Northern Ireland guilty of rushing their final ball at times.
Johan Simun Edmundsson of Newcastle threatened midway through the half with a skidding drive that Lee Camp was only able to push back in front of him on a greasy surface.
Luckily for the hosts, there were no attackers following up the loose ball.
Healy provided 40-year-old Faroes goalkeeper Jakup Mikkelsen with a straightforward save after a good cross from Grant McCann and the pair linked up again after half an hour.
This time a neat pass from Healy sent McCann charging into the area but saw a penalty appeal rightly rejected after minimal contact from Jonas Tor Naes.
McCourt proved the home side's creator again just before the break when he surged towards the Faroes goal before laying off for Healy.
His first-time effort rattled the base of the post after a goal-saving touch from Mikkelsen.
McAuley did not emerge for the second half, replaced by Craig Cathcart due to a virus he had carried into the match.
It looked like Worthington would need to send on a second replacement when Clingan went down under a heavy challenge just after the resumption, but the midfielder was able to continue.
Daniel Udsen had a glorious chance to level matters in the 58th minute after good work by Hjalgrim Elttor but he sent his shot sailing over the upright.
McCourt drifted into the area with some wonderful close control moments later only to lose the ball under his feet before getting his shot away.
There was another warning that Worthington's side might need to score again when Camp was almost caught in possession lining up a clearance.
Davis was the man to answer the call, substitute Niall McGinn speeding down the right flank before cutting back for the Rangers midfielder.
He struck the ball sweetly from 25 yards, leaving Mikkelsen to pick it out of the net.
By now, and in no small part down to McGinn's injection of energy, Northern Ireland were playing with some swagger.
No one more so than McCourt, who added a wonderful third five minutes later.
Once again he ghosted into the box from the left wing before Evans' deft back-heel allowed him to curl home from close-range.
By now McCourt was tormenting the away defence, beating men at ease and teeing up Healy with a thrilling run only for the striker to mis-kick with the goal at his mercy.
There was expectation in the air every time McCourt picked up the ball now and he had one more glorious trick up his sleeve in the 88th minute.
Once more he turned his marker inside and out before bearing down on goal and producing the most sublime of chips that left Mikkelsen clawing at the air and Windsor Park hailing a new hero.