The visitors produced an all-round poor performance, with some slack bowling allowing Linlithgow to reach an imposing 215, before Gala slumped to 81 all out.
Gala captain Dinesh Tharanga had no hesitation in bowling when he won the toss on a damp wicket after a week of rain.
A sloppy start allowed Linlithgow to get off to a fast start on a difficult pitch until Duncan Millar brilliantly stumped in-form Gregor Thomson for 10 off the bowling of Rory Hancock.
Brookes and Stump rebuild the innings before the latter was given out lbw, but Brookes proved key to the Linlithgow innings as he batted sensibly while his team-mates attacked at the other end.
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With a number of boundaries being hit on the small Boghall pitch, there were also some decent catches from Hancock, Finlay Rutherford and Jamie Crooks. But Brookes finished not out for 75 to guide Linlithgow past 200.
Hancock took 3 for 39 while Scott Evans (2 for 41) was unlucky not to claim more wickets from his nine-over spell. Millar and Rutherford started off positively, with both openers hitting a big six each.
But, when both fell in quick succession, it made a difficult task even tougher.
In the end, Gala slumped to 81 all out, with Hamilton claiming a 4 for 5 in a superb spell as Linlithgow claimed a deserved win to leave the West Lothian side as the only team in Division One with a 100 per cent record.
l Another youthful Gala/Hawick Development team suffered defeat to table-toppers Drummond Trinity by 144 runs.
With heavy rain in Edinburgh during the week, the match was switched to Meigle Park but the hosts were under the cosh early on as openers Gurjeet (87) and Pradeep (82) put on 164 for the first wicket.
Gala/Hawick did well to claw themselves back into the game however, as the returning pair Craig Thomson (2 for 39) and Alex Hastings (2 for 44) pegged back the visitors, with the aid of two catches by Maisie Maceira, who also bowled well alongside Fergus Hastings.
The homesters got off to a solid start with Stuart Skeldon (14) and Jamie Bell (10).
But a succession of wickets fell before Paul Cowan (21) top scored to help Gala/Hawick finish on 86 all out.