It was Gala's Sri Lankan professional Upul Indrasiri who did the damage, taking an incredible six wickets for just one run as Kelso were all out for 35.
Gala knocked off the runs without losing a wicket for the second week in a row to remain just ahead of Carlton 2s, who defeated Morton by six wickets.
Kelso chose to bat first and captain Callum Davidson (16) looked in good form.
But, when he was trapped lbw by Indrasiri, the home side's innings crumbled.
Alongside Indrasiri, Dinesh Tharanga took 3 for 22.
In reply, Sid Ponneri (25) and Finlay Rutherford (13) completed the run chase inside six overs to give Gala all 20 points.
A Braw Lads spokesman said: “A tough day for Kelso – of which Gala have experienced plenty in the Championship in previous seasons – which, hopefully, the Tweedsiders can bounce back from.”
There was a more even contest at Meigle Park, as Gala 2nds lost out by three wickets to Edinburgh South 3rds in ESCA Division Seven.
Gala batted first on a glorious day and made a decent total of 155 for seven wickets from their 40 overs, with John Imray (54) and Max Hastings (47) both in good form.
Sharam Reddy (2 for 13) was best bowler for Edinburgh South.
Gala then reduced their visitors to 62 for 6 thanks to a brilliant bowling display by Liam Skeldon, as the teenager claimed his first five-wicket haul.
But a 61-run partnership between Jaskaran Singh (35 not out) and Anuza Suziyapperuma (26) pulled Edinburgh back into the contest.
When Suziyapperuma was dismissed, Jeremy Blood (13 not out) joined Singh to see South home in the 37th over.
The other Gala wicket takers were Robbie Paterson (1 for 29) and Stuart Anderson (1 for 12).
And on Sunday, Gala missed out by eight runs in a thrilling Development League game against Grange 4ths, with Finlay Rutherford scoring a half century, and Liam Skeldon and Kieran Toor taking two wickets each.
C. Davidson lbw b U Indrasiri 16
J. Flannigan-Stubbs lbw b D. Tharanga 5
C. Scott b D. Tharanga 0
C. Adams lbw b D. Tharanga 0
J. Gibson lbw b U. Indrasiri 0
M. Mason b U. Indrasiri 3
G. Ford not out 2
B. Rock lbw b U. Indrasiri 0
K. Jackson st J. Crooks b U. Indrasiri 0
N. Mallen b U. Indrasiri 0
Extras – 9
Total – 35 for 10 wickets
S. Paterson 2-0-11-0; D. Tharanga 6-0-22-3; U. Indrasiri 5-4-6-1.
S. Ponneri not out 25
F. Rutherford not out 13
Extras – 1
Total – 39 for one wicket
C. Adams 3-0-21-0; C. Davidson 2.5-0-17-0.