A second-half strike by forward, Richard Mealey sealed this scrappy game for Fleet, to keep his side in a mid-table position.
The win came as a welcome relief for Fleet boss, Mick Catlin, after seeing his side mauled 5-0, in midweek, away at Croydon Athletic.
Catlin now has a week to prepare his side to make a winning start to the FA Trophy competition next Saturday at Calthorpe Park.
Saturday's match at Banstead started badly for Fleet, when new signing, keeper, Justin Gray had his clearance blocked and it fell to the feet of Banstead striker, Neil John, who neatly slotted home the opener after only two minutes.
Fleet rallied well, and should have equalised when Shaun Hale's powerful shot was well-saved by Banstead keeper, Adrian Blake. It was Hale though who finally got the equaliser on the stroke of half-time, when he headed in a Gary Connolly free-kick.
Both sides struggled to make headway after the break, until on 77 minutes Mealey's strike sealed things after the 21 year-old striker beat the offside trap to score from close range.
There had been less joy for Fleet on Wednesday night when they came up against an in-form Croydon Athletic.
Fleet started brightly, but conceded twice within 5 minutes, after almost 30 minutes of fairly even play. The first on 29 minutes came after Croydon's James Evans rounded three defenders to score from a tightish angle.
Five minutes later it was Croydon's defender, James Hall who got up unchallenged to head in from a corner.
Croydon added a third immediately after the interval, when a series of missed tackles allowed James Greenaway to score from close range. Five minutes the same happened, after Fleet failed to clear the ball, and Danny Stassinos easily beat keeper, Peter Houkes to net his sdie's fourth.
The home side completed the scoring with only a minute to go, when Hall netted his second, again with a header.
