Johnston was only introduced five minutes prior and was on hand to prod home Kelvin Langmead’s near post header as the Southern League (Premier) side advance.
“We’re devastated,” manager Steve Chettle said. “The players are devastated; the players are devastated, and the club are devastated.
“We did enough to win the game and I didn’t think at any point really see them creating too much - I think Adam [Collin] has made a couple of saves but that’s it.
“This game’s beautiful,” he added, with a wry smile.
“We spoke to the lads before the game and told them that they have no divine right to given anything in football and you have to see the game out.
“It’s tough to take today. There’s a bit of a sour taste in my mouth.”
Basford started the brighter of the two sides and that continued throughout as they did everything but trouble Jack Harding in the away goal.
Aaron O’Connor intercepted a lazy pass from Connor Roberts in the opening minutes to set up captain Matt Thornhill who sliced wide.
Ryan Wilson then found O’Connor with a wicked cross deep from the left, though the striker’s header – deft – angled wide.
On the contrary, those from Oxfordshire did very little to trouble Adam Collin in the home goal.
The imposing figure of Chris Wreh – son of former Arsenal and Liberia Striker of the same – began to cause some issues but Owen Betts did excellently to deflect the front man’s very dangerous cross behind after 13 minutes.
Moments later, at the other end, Kane Richards skipped around the committed Brown, advanced and the lay-off to O’Connor looked certain, but for an overhit cross saw the chance wasted.
Controversy followed five minutes later when United had the ball in the net through Richards’ header from Wilson’s corner; only referee Dane McCarrick saw an infringement on ‘keeper Harding to curb all jubilant celebrations.
Home pressure continued and – in a carbon copy to his goal at Warrington on Tuesday night – Brad Gascoigne set himself from another Wilson cross, took aim and fired a low shot through a body of players which Jack Westbrook hacked desperately clear.
A rare foray forward saw Ben Aquaye break down the left with pace and ultimately find the onrushing Harry Reilly whose shot was tame and easy for Collin in front of a soddened, yet buoyant, 514 at a rain-soaked Greenwich Avenue.
Both sides enjoyed chances early in the second half.
Wreh did well to turn and shoot at Collin’s goal; saved. And Matt Thornhill must’ve thought his 65th minute strike from 12-yards out was the opener but for a floored teammate in Marcus Marshall who inadvertently blocked.
O’Connor then had a fine opportunity on the end from Terry Hawkridge’s pass to put the hosts in front, but Harding was just about equal to the effort, smothering with his backside.
As the seconds ticked, and with those in attendance on tenterhooks, a cheap free kick was hoisted in, Langmead flicked on from Wilson’s upward header and Johnston was alive to stab the loose ball past Collin to send the away support into raptures and Banbury into the Fourth Qualifying Round.
FC United of Manchester are the next visitors to Greenwich Avenue on Tuesday, October 5 in the Northern Premier League (19:45).
BASFORD UNITED: Adam Collin, Owen Betts, Ryan Wilson, Dom Roma, Brad Gascoigne, Declan Dunn, Terry Hawkridge, Matt Thornhill, Marcus Marshall, Kane Richards, Aaron O’Connor
SUBS NOT USED: Alex Howes, Rev James, Jordan Haywood, Stef Galinski, Jordan Pierrepont (GK)
BANBURY UNITED: Jack Harding, Connor Roberts, Sam Brown, Alex Babos, Kelvin Langmead, Jack Westbrook, Harry Reilly (Henry Landers 72’), Giorgio Rasulo, Chris Wreh, Morgan Roberts, Ben Aquaye (Ethan Johnston 84’)
SUBS NOT USED: Theo Rowe, Ben Taylor, Brandon Patterson, Tom Rowley, Tom Sharpe