Australia began the defence of the title they won 11 months ago with a crushing defeat to Trans-Tasman rivals New Zealand and now face an uphill climb to finish in the top-two of their Super 12s group.
England made hard work of overhauling Afghanistan's 112 all out but did so with five wickets and 11 balls to spare and will next face Ireland on Wednesday before taking on Australia at the MCG on Friday.
While Curran was adamant England will not look past their next opponents, a grin spread across his face as he contemplated handing Australia a defeat which could end their hopes of reaching the semi-finals.
"Ireland are obviously going to be another very tricky game," said Curran of a side who defeated Scotland and the West Indies in the first preliminary round to reach the main Super 12s stage.
"We've seen the way they played in the qualifiers, they're obviously a very dangerous team with some match winners in there as well. We'll focus just on Wednesday's game.
"But there's there's no hiding that Friday is going to be a pretty epic game against Australia, at the MCG, which I'm sure will be an incredible experience for all of us.
"Hopefully we can go into that game having won on Wednesday and, if we win, that will be obviously great for us and I guess might put Aussie in a tricky position."
Curran's five-wicket haul in Perth on Saturday was the first by an England male bowler in T20s as Afghanistan lost their way dramatically, having been 81 for three after 14 overs before being all out with two balls unused in their innings.
The left-arm seamer has developed a reputation for being dependable at the death on this trip to Australia, his first with England, and finished the innings with four wickets in his last six balls.
"It's a fantastic win for us," said Curran, who missed the last World Cup in the United Arab Emirates after suffering a stress fracture in his back a couple of weeks before the tournament began.
"It's my first World Cup game and the energy when I woke up, to know that you're going to be playing in a World Cup gives you that extra bit of buzz having missed the last one.
"These Australian decks, it's my first time playing here as well so I'm really enjoying the bounce and the pace and you can use the dimensions of the ground as well. I'm really enjoying it.
"There will be some days where it doesn't come off which I'm very, very aware of but hopefully I can keep taking confidence and all the other bowlers around me can taken confidence from that performance."
Ben Stokes took two for 19 while Mark Wood also collected two wickets and averaged 92.6mph on a springy pitch with plenty of carry - the fastest four-over bowling performance in this tournament's history.
A complete bowling performance was backed up in the field as Liam Livingstone, Moeen Ali, Adil Rashid and Jos Buttler took highlight-reel catches before England's batters laboured in their chase.
After 14 overs, England were on 81 for four but the decision to stack their batting meant a dramatic collapse akin to what happened to Afghanistan was never on the cards and Livingstone's unbeaten 29 off 21 balls proved priceless in a low-scoring encounter.
"We knew Afghanistan were going to be that type of side and we were going to have to scrap really hard for those runs in that chase," added Curran."The boys got us home which was good.
"We knew that we had to respect the Afghanistan bowlers, they had some incredible bowlers out there, but I think the main thing is a win. So we're very happy."