Teenage midfielder Joe White opened the scoring for Newcastle's youngsters, completing a fine attacking move for the visitors with a drilled finish, before Ruben Shakpoke's close-range finish on the stroke of half-time drew the Villans level.
Josh Scott regained United's one-goal advantage, netting his third league goal in as many league matches, before Newcastle's second-string withstood a late attacking surge from the hosts to register their first away victory of the 2022/23 campaign.
Turner-Cooke, who joined Newcastle's Academy from Sunderland in January 2021, told nufc.co.uk: "We're very pleased with the three points. Our last result against Middlesbrough (a 1-1 draw) was a bit disappointing, conceding in the last minute, and we had to dig deep against Villa to come out on top and thankfully we did that. We're all very happy!
"The start to the season wasn't the best but we knew that. The last few games, we've done very well in spells and you can see, as each game comes, we're putting that more together for the full 90 minutes.
"Villa have a good team so when you come away, you know it's going to be a good test. We went out, played very well and buzzing to pick up three points."
Newcastle faced a double injury blow against their Villans counterparts as 16-year-old midfielder Lewis Miley, making his first start for United's under-21 side, was withdrawn in the opening 20 minutes before top goalscorer Dylan Stephenson, who has netted four goals so far this term, hobbled off during the second-half.
Turner-Cooke, born in South Shields, commended his side's effort despite a number of setbacks throughout the Division Two encounter and revealed he had recently overcome a bout of illness before carrying out a spirited display in Warwickshire.
The 18-year-old, who travelled with the Magpies' first-team squad on pre-season trips to Austria and Portugal last summer, added: "We weren't too down at half-time. It was a rubbish time to concede, just before half-time, and it probably came from our mistakes which could have been preventable.
"However, we knew we were playing well and had the players at the top and middle end of the pitch to score goals and Scotty (Josh Scott) came up with that.
"We had Lewis go off in the first-half, which was a blow, but we stuck together and then we saw Dylan come off injured. I've trained twice in the last week and a bit as I've been ill but we all had to stick together.
"That's the character the boys have got - we dig in for each other and we're absolutely delighted that has resulted in three points."
