Marcus Dinanga and Ste Wearne had given the hosts a 2-0 lead at the break at Gateshead International Stadium, where heavy rain made for a tricky encounter against the National League side.
But Eddie Howe's charges responded well after the break, with Elliot Anderson and Allan Saint-Maximin drawing them level before Lewis Miley picked out fellow substitute Turner-Cooke for the well-taken winner.
An action-packed opening quarter of an hour brought an opening goal and a flurry of chances. Matt Ritchie had the first, firing wide inside ten seconds before seeing a header diverted past the post by Louis Storey.
A fine opportunity fell Sean Longstaff's way soon after, when lone frontman Saint-Maximin found him with a neat through ball. The midfielder's initial attempt was well stopped by goalkeeper Achie Mair, though, and he didn't connect well enough with the follow-up to find the target.
Gateshead looked bright, however, and Dinanga had a first sight of goal when Dan Burn miscued a pass and let him through on goal. Burn recovered well and just about got enough of a touch on the ball as the Heed's forward tried to cut inside him and pull the trigger, but it was something of a warning about what was to come.After Jamal Lewis scuffed a Saint-Maximin centre wide and Adam Campbell, another ex-Magpie, had a speculative shot saved at the other end, the hosts took the lead. It came from a Newcastle error as Longstaff surrendered possession around 20 yards out, and after being played in Dinanga took full advantage, drilling a shot low beyond Karl Darlow in the United goal.
Another mistake then gave Callum Whelan a sight of goal, but he dragged his effort before a brief spell of Newcastle dominance - Saint-Maximin forced Mair into a terrific save with a powerful shot from inside the box and Longstaff bursting into the area only to clip his shot wide.
But on the stroke of half time, Howe's men fell further behind. More uncertainty at the back led to Wearne evading Darlow's grasp and planting his shot low into the left-hand corner to leave the visitors with plenty of work to do.
Amid dire conditions, with thunder and lightning following heavy downpours, Loris Karius and Alex Murphy were introduced at the break as play continued despite the weather. Five minutes after the restart, they pulled a goal back as Saint-Maximin slipped a pass inside to Anderson. The youngster managed to cut inside his marker and keep his footing, sending a low sidefooted effort beyond Mair to cut the deficit.
Saint-Maximin, playing centrally in attack, then whipped one just beyond Mair's left-hand upright and some more magic from the Frenchman almost brought a leveller as he danced past the Heed's defence in the box, but couldn't quite provide the final pass.
Eventually, though, the equaliser did come, and it was Saint-Maximin who got it. This time it was Gateshead's turn to gift their opponents a chance, and after the hosts gave the ball away cheaply, Longstaff played in Anderson. He showed composure to pick out his teammate in the middle, with the Magpies' number ten applying the finish.
Saint-Maximin was enjoying himself, and almost provided a third for Anderson seconds later, but the resulting shot was well blocked by Mair, before Campbell saw his own attempt deflected to safety.
Howe then made some changes with 25 minutes remaining, introducing five youngsters, including debutants Harrison Ashby and Ben Parkinson, and another of those replacements could have given Newcastle the lead within five minutes of his introduction. Lucas De Bolle found himself on the end of a flowing move but couldn't slide his shot beyond Rob Elliot, the former United stopper sent on as a substitute by Gateshead.
There were further debuts handed out to Michael Ndiweni and Charlie Wiggett, but it was another young player who made the most decisive contribution. Turner-Cooke arrived at just the right time to sweep home Miley's terrific pass beyond Elliot and complete the turnaround, netting his first senior non-competitive goal in the process as Howe's side began pre-season with a victory.
There was a memorable moment for the Miley family in the closing moments, too, as Jamie Miley came on for his own bow to play alongside his younger brother Lewis.
Newcastle United: Karl Darlow (Loris Karius 46), Kieran Trippier (Harrison Ashby 65), Javier Manquillo (Michael Ndiweni 72), Remi Savage (Alex Murphy 46), Dan Burn (Jamie Miley 84), Matt Targett (Lewis Miley 65), Jamal Lewis (Charlie Wiggett 77), Sean Longstaff (Lucas De Bolle 65), Elliot Anderson (Jay Turner-Cooke 72), Matt Ritchie (Ben Parkinson 65), Allan Saint-Maximin (Joe White 65).
Subs not used: Mark Gillespie.
