Wooden goal decisive but Moneyfields could have won by a bigger margin
Wooden struck just past the hour mark to give the home side their third successive league win.
The Southern League division one south finished closer than it could have done if chances were taken.
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Hide AdCarter's side climbed up to seventh spot with games in hand on the teams above them.
But the boss felt they ought to have scored more.
He said: '˜We were in control throughout the game.
'˜Our finishing, however, was not the best.
'˜Though we beat them heavily in a cup game at their place recently we knew this would be tougher.
'˜They got plenty of players behind the ball and we had to be patient to break them down.
'˜When we needed to be we were good in defence.
'˜We had to work hard for it but we were good value for our win.'
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Hide AdThe home side suffered a blow after only three minutes when defender Brett Poate limped off with a calf injury.
Later fellow defender Curtis Da Costa dislocated his shoulder for a second game running.
Dan Woodward, Felipe Barcelos and Steve Hutchings all missed good chances in a first-half which ended goalless.
On 65 minutes Steve Mowthoroe came to his sides rescue with an outstanding save.
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Hide AdThe home goalkeeper got down well to hook a goal bound shot out of the bottom corner.
Wooden provided the decisive strike with a 25-yard shot which went in via the crossbar and post.
Hutchings and Wooden had further chances but failed to make the most of them.
Carter added: '˜We have hauled ourselves up the league and have three more home games to follow.
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Hide Ad'˜It is good to have Hutchings and Wooden finally getting back to full fitness.
'˜We will probably be without Poate for a couple of weeks.'
Moneyfields have a chance to climb into the play-off places on Tuesday night when they host Melksham Town at Dover Road (7.45pm).