Grant Goodhead's goal, here pictured entering the net eight minutes from the end, earned Town a handy £1,500 FA Cup boost with the prospect of another good payday when they visit Leamington in the next round.
Town can expect to play before a crowd of over 500 - a marked contrast to this game in which their own supporters must have come close to outnumbering the home fans.
A difficult crossfield wind, firm drying ground and, perhaps, the pressure of playing for a much-needed prize pot of cash got to both teams.
Both started reasonably well but as the conditions worsened, the harder they tried to get control, the more both sets of players lost it.
Frustration boiled over in the home camp to such an extent as tension mounted towards the end that the referee had to take some of their squabbling players to one side and deliver a lecture.
It didn't work too well for they continued arguing among themselves with a vehemence that must have contributed to the deciding goal, moments later.
Town, sticking to their task well amid the distractions, earned follow-up possession when a set piece was only partially cleared and Goodhead, on the edge of the area, powered a well placed winner into the net.
On balance and considering they were again badly hit by injuries and absentees, Town deserve praise for earning their pass to Leamington - but the game itself was one they will be happy to have behind them.
Everyone worked hard for this, their fourth successive victory and, individually, it must be said that all had their moments.
Skipper-keeper Andy Pryce made a some of fine saves again but mirrored the see-saw fortunes of his team mates by being dead lucky to get away with watching a shot skip past his far post.
His defence mixed some magnificent tackling with suicidal clearances and the midfield and attack managed moments of bravery and near brilliance with some lapses a more switched-on opposition might have cashed in on.
So, overall something of the much-quoted curate's egg - but the really encouraging aspect from Town's viewpoint is that they fought hard for each other throughout, understood, even forgave each other's mistakes and, unlike Stone, stuck together superbly in a way that many teams will find hard to beat.