The bonus-point win put Northampton into third ahead of Midlands rivals Leicester but the thumping match could have gone either way as the second half ticked down.
Irish got tries from full-back Delon Armitage, wing Sailosi Tagicakibau and flanker Declan Danaher, with Adrian Jarvis booting eight points.
Saints went over the line via wing Noah Cato, number eight Roger Watson, full-back Paul Diggin and Nutley's winner, with outstanding Stephen Myler adding 10 points with the boot.
Irish desperately wanted to win after their coach Toby Booth demanded a massive turnaround in his side from the one which lost 19-10 at basement outfit Newcastle last weekend, going as far as to issue an apology for the performance.
And, with Northampton looking to pile the pressure on Leicester in the top four, the Exiles knew they had their work cut-out to take the much-needed victory.
Myler was on fire all game and set up the first of his side's tries for Cato with 11 minutes gone with a long pass wide to the left that had the home defence bemused and the winger in at the corner.
It was a tactic he would used twice more during a thrilling game.
Irish, not wishing to have the wrath of Booth for a second successive week, hit back with a vengeance in the opening period.
Their New Zealand ace Tagicakibau, playing only his third game since injury, was the catalyst for their dominance, while England ace Armitage also came good.
The two players combined as Irish took a 10-5 lead near the half-hour as Tagicakibau bulldozed his way down the left wing to pass inside for Armitage. Saints wing Vasily Artemyev was in close attendance and agonisingly saw the ball bounce off his knee for the home full-back to gather and score.
Then the boot was on the other foot as Jarvis, who had kicked two penalties and a conversion by then, hammered up a high ball from half-way for Armitage to chase.
He missed the pick-up but wing Topsy Ojo was on hand to keep the move going and feed his fellow wing for a try that put Irish 18-8 up before Myler kicked a second penalty of the half to reduce the arrears.
Almost immediately after the break, the Saints really did start marching and put a stranglehold on the Irish defence for the early part of the half.
It paid off in points as Myler's earlier try-scoring pass tactic was deployed for number eight Roger Wilson to stroll over from five metres on the right wing.
And he made it a treble when an attack reached the home line and Myler sent Diggin over on the left wing.
That put Northampton into the lead for the first time, but their 23-18 lead did not last long as the pulsating clash became white hot.
Irish lock Nick Kennedy went galloping down the left wing to threaten a score but, after he was caught, the Exiles moved the ball across their backs for Armitage to again play the part of provider and put Danaher in with a 15-metre run down the right touchline.
There was everything to play as the match ran down and the scores locked at 23-23. Both sides looked for gaps to break the deadlock but, even with tired limbs, neither would give away the chance.
But with four minutes left and Northampton finishing the stronger, Irish gave away a crucial penalty. However, the normally reliable Myler pushed the kick wide of the uprights.
Nutley's winning score came two minutes from time and was a charge down that England would be pleased with as Armitage's clearance kick was blocked by centre George Pisi who collected and passed to waiting Nutley to take the victory.
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