Melton trailed 18-12 with less than 10 minutes left of a tooth-and-nail final against Hinckley, a side who play two leagues higher in the pecking order,
And when Cox’s tough conversion of James Woolley’s late try fell inches short, that seemed to be it.
But one last hurrah upfield saw Hinckley penalised for holding on and Cox held his nerve to secure a dramatic 20-18 win with the very last kick.
With Hinckley shorn of several players at kick-off, stuck in traffic, Melton started at a lightning pace and were ahead within three minutes.
Progress was made up the middle through the forwards before play was spread out to the left. A transgression allowed Cox to put over a simple penalty.
Minutes later Sam Badham came within a few metres of the opening try as he burst through the middle in barnstorming fashion. Badham carried two players with him, but was hauled down just short and the move broke down.
Hinckley began to enjoy more possession and looked certain scorers, but for Harry Wood’s brilliantly brave block under pressure from two opponents.
But the space was beginning to open up for Hinckley’s nippy backs to exploit, and Branson’s quick break down the left put in Joe Glover for a simple run in midway through the half,
Hinckley began to control possession, but were repelled by some brilliant defence. Repeatedly Hinckley kicked their penalties to touch, but were held up and forced back.
They finally decided to kick for the posts minutes before half-time when Cox was penalised and sin-binned for not rolling away.
Lord’s penalty opened the gap to 8-3, but Melton hit straight back. A brilliant high catch gave them good territory before further disciplined pressure forced a penalty.
Harvey Green sent Melton in the more buoyant at half-time with an accomplished penalty with the last play.
Hinckley came out of the blocks fast after the restart, but Melton struck first after a dropped catch forced Hinckley to concede a lineout five metres from their own line.
A trademark catch and drive was stopped, but Rose put Cox through a gap and he appeared to have scored. However, they again they had to settle for three points via Cox’s straightforward penalty and Melton were back in front at 9-8.
Melton’s defence continued to stand tall under what was, at times, relentless pressure with Mark Matthews making several crucial last-ditch tackles.
But midway through the half, Hinckley finally found a chink in the armour, exploiting the smallest of gaps to sneak through under the posts for a converted score and a 15-9 lead.
If spectators thought that may at last open the floodgates, they were wrong. Tireless Melton hit back.
After another lineout was won deep within the opposition 22, Melton’s pack drove Hinckley back over their own line.
They appeared to be held up, but a penalty was the result and Cox reduced the arrears again to 15-12.
Hinckley battered the Melton line with pace and power, but the defence somehow held back the tide.
With a little over five minutes to go, Glover finally decided to go for the posts and established a seemingly decisive 18-12 lead.
But, incredibly, back game Melton. Wood’s thrilling burst through the middle and hand-off to Woolley took them 20 metres into their opponents’ half.
Two more lineouts were earned close to the line, but both times Hinckley’s flagging defence held out brilliantly. But only just.
Hinckley were reduced to 14 after Wood was upended as Melton once more tried to outflank their National League opponents.
Another surge over the line failed, but the try came in the dying minutes, Woolley finally getting around the back of the Hinckley rearguard to dot down.
When Cox’s match-winning conversion from out wide fell just short, that appeared to be that, but Melton summoned up one last effort, kicking to touch to return to the familiar turf of Hinckley’s 22.
Hinckley appeared to extinguish all hope when they won they took the throw, but referee Joshua Burgess blew his whistle once more.
Deciding Hinckley were holding on, he awarded Melton a chance to win it. Cox stepped up and made history.
Updated 15:53 - 21 Jan 2018 by Matthew Grice