The Surrey seamer showed nerves of steel to see the hosts over the line in front of 55,000 fans, taking 5-35 to cap a 4-1 series win over Australia.
England scrambled to 259 batting first on an unpredictable drop-in surface – Jason Roy thrashing a quick 49 and Yorkshire’s Joe Root applying a more studious method for his 62 – and appeared to have lost control of the chase when Australia reached 192-4.
But Curran led a stirring comeback, seizing the moment and scattering the tail to seal a 12-run triumph.
“What a stadium, what a day and what a team to be a part of,” the 22-year-old said as he soaked up his achievement.
“It’s a very special day. That’s what we train for. You want to be asked to perform in the big moments and to be involved when the game can go either way, that’s when you get the most satisfaction.”
Curran was kicking his heels for the first three matches of the series, earning his call only after the trophy had been won following an injury to Liam Plunkett.
But, on just his third ODI appearance, he made it clear he is eager for more.
“It was very frustrating, but if you’re getting left out as a player and you’re happy about it ... international sport is probably not the place for you,” he said.
“I’m just looking to take these moments. It’s a pleasure to be part of this side.”
Curran’s efforts nudged Perth local Andrew Tye into the shade, though his 5-46 in the first innings will at least earn him a place in the history of his new home stadium.
Tye might easily have been the one celebrating a match-winning turn had Jake Ball been unable to bowl his final two overs, with England almost losing the seamer unexpectedly at the denouement.
“He was feeling very dizzy and nauseous, he couldn’t really keep his balance,” captain Eoin Morgan revealed.
“The doctors got him off and did a great job with him to get him through an over.
“It was key for us because we would have had to go to Joe (Root), which would have been a big moment.”
On the latest emerging star in England’s white-ball ranks, Morgan added: “To see Tom bowl a spell like that as such a young guy is a great sign.
“We’re spoilt for choice at the moment. Guys are fighting for positions left, right and centre.”
Australia’s Steve Smith, who has gone from a conquering hero in the Ashes to an embattled batsman and captain since switching formats, insisted he had the appetite to revive his side’s fortunes.
England operate a split system, with Root leading in Tests and Morgan in one-dayers, and there are growing calls Down Under for a similar approach.
“I’m happy leading these boys at the moment but, unfortunately, I haven’t done as well with the bat as I’d have liked,” he said. “Me and Davy Warner, as the senior players, haven’t stepped up and that really hurts the team. But I’d like to keep taking this team forward and doing the best I can.”