The young Magpies took the lead against the League Two outfit in the latter stages of the first-half, following Ben Parkinson's header, but Olly Sanderson's leveller before half-time and Andy Cook's close-range finish turned the Northern Section Group H clash in the Bantams' favour.
However, Donaldson sent the clash to a penalty shoot-out after the Gateshead-born striker inadvertently turned Jay Turner-Cooke's free-kick into the net in stoppage-time before successful spot-kicks from Parkinson, Turner-Cooke, Huntley and Donaldson saw United's second-string prevail on penalties, with Magpies goalkeeper Aidan Harris denying Alex Pattison and Cook from 12 yards.
The 18-year-old forward, who joined United's Academy in 2019, told newcastleunited.com: "It's class to come to a League Two team, a strong side, and it was a different challenge for us but we've got a good all-round squad, with players not even in the squad who are very good as well.
"We're not surprised to come and win here but it is a big result for the group. The way we won shows the team's character and we want to build on that now going into the next group games. Hopefully, we can go far in this tournament.
"It's such a great experience coming to the stadiums and playing against a big club in Bradford. They play in the Football League and, ultimately, that's where we want to be in playing professional football in England. It's a great stepping stone for us."
Donaldson, who scored on his under-21s debut during a Premier League Cup clash against Huddersfield in September 2023, praised Harris following his goalkeeping heroics in the penalty shoot-out, with United now sat in second spot of their respective group, which involves 2022 winners Rotherham United and Mansfield Town, on two points.
The teenage forward is also hopeful the youthful squad can build on their experiences against senior opposition as the young Magpies aim to qualify for the competition's knockout stages for the first time since 2018/19 as a squad involving Sean and Matty Longstaff ventured to the last-16 before exiting against Sunderland.
He added: "Aidan's class! He made some great saves in the shoot-out and we have a lot to thank him for. He's got so much potential and he's a great lad as well.
"It was great to win on penalties but I don't think the pressure was on us. They're a senior team and we're young lads so we just had to brave in taking our penalties, which we were, and managed to win the shoot-out.
"It's one of the first wins the club have had in the competition for a number of years so, hopefully, we can take belief from this game and try to win the next matches coming up."
