Chasing 153 for victory, Banton's 63 off 41 deliveries guided England over the line on Saturday after Scotland made early inroads into their top-order.
"It's T20 cricket, it's a high-risk game and you've got to keep backing yourself," said Banton, who picked up the player of the match award after falling early against Nepal and the West Indies.
"At times, it goes against you and it's hard, you've got to keep coming back, keep trying hard, keep practising. Luckily, today was my day."
England won the toss and elected to field, with pacer Jofra Archer picking up two wickets in his second over to dismiss George Munsey and Brandon McMullen while Michael Jones fell in the powerplay for a quickfire 33.
Richie Berrington and Tom Bruce (24) steadied the ship with a 71-run stand, a measured counter-offensive that targeted the spinners and increased the run rate to nine per over.
Both fell in quick succession, however, with Berrington out one run short of what would have been a hard-earned fifty when he was trapped lbw by Adil Rashid (3-36).
From a relatively comfortable 3-113, Scotland stumbled into disarray as the duo's wickets triggered another collapse but Oliver Davidson offered a final flicker of resistance with an unbeaten 20 that took Scotland to 152 all out.
"I thought we fought back really well after losing those early wickets," Berrington said.
England's chase got off to a poor start when the explosive Phil Salt fell to the third ball of the innings and fellow opener Jos Buttler was dismissed in the second over.
Banton and Jacob Bethell (32) shared a 66-run stand but Scotland struck twice again when Bethell and captain Harry Brook (four) attempted to play sweep shots and were caught.
That brought Sam Curran to the crease and the allrounder who's having a fine World Cup again eased the pressure with a knock of 28 before he fell skying a Brad Wheal delivery to wicketkeeper Matthew Cross.
But Will Jacks (16no) finished the chase in the penultimate over with the game's biggest six and a four.
