Wealdstone started the brightest of the teams and they should have led just 2 minutes in when Danny Green played Dan Fitchett in on goal. but the striker hit straight at James Hamon when one on one.
The home side`s Iffy Allen proved to be a handful in the opening stages, crossing for Ricky Wellard, who headed wide, and also creating an opportunity of his own that he blasted just wide of the post.
Gloucester defended well though with blocks from Robbie Cundy and Sam Avery denying threatening opportunities from Green and Allen.
And on 37 minutes they took the lead. Joe Hanks played a defence-splitting ball to Harry Williams (pictured), he cut it past Reagan Ogle and slotted underneath Jonathan North in goal.
This encouraged the Tigers and they took that momentum into the second half.
North had to be alert twice to deny Hanks before a goalmouth scramble ensued with the keeper eventually punching the ball out for a corner.
From the resulting corner the lead was doubled. Ed Williams played it short to Banks, he beat Wellard and fired a hard, low shot with pace across goal and the slightest deflection took it out of North's reach.
Wealdstone gave themselves a lifeline on 73 minutes. Wellard had a shot blocked and Gloucester failed to clear their lines properly, allowing Fitchett to pounce on a loose ball and fire into the top corner from close range.
The visitors almost restored their two-goal margin instantly, but North was out quick to deny substitute Joe Parker from point-blank range.
Stones mustered up late headed chances from Mustafa Tiryaki and Fitchett, but a late equaliser would have been harsh on the visitors who showed immense work-rate throughout the contest.