With eight minutes of second-half added time, United threw everything at a resolute Southampton Women's defence and when the visitors failed to clear a corner and after some pinball in the box, Cooper poked home from close range.
Southampton came flying out of the traps and looked to quieten down the Geordie crowd, something they managed to do after just seven minutes.
Freya Gregory charged down Claudia Moan's attempted clearance and with the ball having fallen nicely to the feet of the attacker, she had the simple job of tapping into an open net.
Southampton almost doubled their lead three minutes later when Molly Pike used her pace to get in behind the United defence, but Moan managed to tip her audacious effort onto the crossbar.
After surviving an early wave of pressure, United began to grow into the game and almost found themselves level just before the half-hour mark through Katie Barker.
United's number nine picked up the ball midway in the Saints' half before dancing past two defenders, but could only watch on as her long-range effort crashed off the bar and behind for a goal kick.
The game continued to be very open with the Saints almost going 2-0 up but Moan produced a stunning diving save to deny Pike from an acute angle before Demi Stokes blocked the rebounded effort on the line.
Some robust pressing from the front presented Shania Hayles with the ball inside Southampton's 18-yard box, but after feinting to go one way she was unable to test Fran Stenson due to Jemma Purfield's block.
It was a more subdued second half, but it was Newcastle who carved open the first half-chance. After working the ball from left to right, Isabella Sibley found Barker in the box, but her effort was well blocked by the Saints.
The game began to kick into life after the hour mark and United fan and captain Amber-Keegan Stobbs saw the ball land at her feet in the box after Southampton failed to clear a free kick, but with Stenson rooted to the spot, the skipper curled her effort narrowly wide.
Newcastle continued to pile on the pressure with just over 20 minutes left to play when Amy Andrews skipped past Purfield in the box to pick out McQuade, but her looping effort - seemingly destined to lob Stenson - was finely tipped over the bar.
The whole of the Gallowgate were on their feet as Beth Lumsden chopped inside Milly Mott to break into the box and fired her low effort goalwards, but they were all left devastated as it rolled inches wide of a helpless Stenson.
It looked as if Newcastle United Women were falling to their first-ever defeat at St. James' Park until the 99th minute.
Southampton failed to clear a Lumsden corner and after two ferocious efforts from Sibley, the ball ricocheted to Cooper who was lurking in the six-yard box, and the defender showed off a striker's instinct to poke past Stenson and send the 11,620-strong crowd wild.
Newcastle United Women: Claudia Moan, Lois Joel (Elysia Boddy 60), Charlotte Potts (Liv Watt 30), Deanna Cooper, Demi Stokes, Amber-Keegan Stobbs, Jasmine McQuade (Sophie Haywood 84), Isabella Sibley, Katie Barker, Beth Lumsden, Shania Hayles (Amy Andrews 60)
Subs not used: Grace Donelly, Emma Kelly, Georgia Gibson, Kacie Elson, Hannah Greenwood