The 20-year-old Manchester United midfielder and younger brother of Jonny who missed the game through injury had been on the pitch for only a few minutes in the second half before scoring.
He marked his first competitive outing by slotting home a cross by Craig Cathcart, who was making his debut, in the 70th minute.
Match-winner: Corry Evans pounces to fire home the only goal of the game
The home side responded and Maik Taylor, 39 today, had to make a good save from Valter Birsa.
Evans said afterwards: 'I haven'tscored for Northern Ireland since I was a schoolboy, so to get on thescoresheet in such an important match is fantastic.
'We've had our criticism over our away form and for not being able to score goals, so to win away with a clean sheet is great.'
Northern Ireland had started the evening brightly and although they then found themselves under pressure for long spells, they were able to get the victory they had craved.
Both sides had early chances that went begging; Valter Birsa shooting wide in the 15th minute for the home side and Chris Baird whipping in a shot from 25 yards that was also off target.
Pure joy: Evans celebrates his goal with team-mate Kyle Lafferty (right)
Slovenia almost made the breakthrough in the 21st minute when Birsa got on the end of a cross from Zlatan Ljubijankic only for Cathcart to make a timely clearance.
Northern Ireland found themselves on the back foot in the 38th minute with Andraz Kirm whipping in a cross. Milivoje Novakovic peeled away from his marker but delivered a soft header from six yards into the arms of Taylor.
This was suddenly a difficult time for Northern Ireland and Kirm sent a ball across the face of the goal but no-one was on hand to take advantage. Birsa then got enough power on his shot from inside the area but Cathcart was handily placed and deflected the ball to safety in the 49th minute.
Back came Northern Ireland and Brunt sent Healy clear down the left nine minutes later. The Sunderland striker cut inside but only succeeded in sending a shot straight at goalkeeper Samir Handanovic.
Mountain to climb: Warren Feeney vies with Slovenia's Bojan Jokic and Bostjan Cesar
It proved to be a brief respite and after another flowing move Kirm's strike from 12 yards was blocked by Baird.
Northern Ireland were defending in numbers and Stephen Craigan then put his body on the line in the 64th minute to keep out a shot from Robert Koren.
Three minutes later Nigel Worthington made a double substitution with Lafferty and Corry Evans coming on Healy and McCann.
Northern Ireland then stunned Slovenia with midfielder Evans, who is also at Old Trafford, scoring at the far post following a glorious cross from Cathcart.
The home side responded and Birsa got into a good position in the penalty area but Taylor, 39 tomorrow, got down quickly to make the save.
Then Ljubijankic found the side-netting from an acute angle in the 81st minute as Slovenia went in search of the equaliser.
Johnny Gorman, who attends Wolves Academy and Repton School, then made his competitive debut a minute from time for Brunt as Northern Ireland held out for a famous win.
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