Set-piece strikes from Darren Timms, Paul Nicholls and Harj Dhesi were enough to see off a Saints side run by assistant boss Steve Johnson in the absence of John Hannah. It was by no means the most compelling of derby contests, but the result, coupled with Saturday's 2-0 win over Meir KA, made Brakes manager Jason Cadden a happy man.
"We've worked hard and it's all come right at the right time. Meir and Southam were both scrappy affairs but we scraped the results.
"Against Southam we were on top for the whole game but we didn't really play as well as we can.
"Still, we've won four games out of four and we haven't conceded a goal - although obviously that will come to an end," he said.
"Saturday is going to be a big test for us, Griff have bought in some quality players. Rugby will be up for it on Tuesday as well, but we'll be going into the week in a good frame of mind."
There was little to choose between the sides in the first half. Dave Care and Vernor Sleem were responsible for many the home side's livelier moments and the returning Nick McFarlane headed just over the bar close to the interval.
Southam bossed the opening stages of the second half without looking too dangerous in front of goal. Stand-in skipper Darren Timms finally broke the deadlock with a header from a Care corner after 56 minutes.
Substitute Paul Nicholls marked his return to the fray with a well-taken free kick which he blasted past unfortunate Saints keeper Dean Merrick.
James Harri and Harj Dhesi came off the bench in the closing stages as Brakes looked to make things safe, with the latter man crashing in a free kick deep into stoppage time.
Johnson saw Monday's game differently from the Southam dugout. He said: "We worked hard, we matched them and we almost got a goal ourselves. We were really up for it and I think we scared them a little bit because they thought we were going to be a walkover.
"After half time we came out more buoyant and carried on from where we left off and we looked as though we were going to get there until with 25 minutes to go they finally got a goal from a corner and our heads dropped a bit.
"It really is only a matter of time before we get that win and put a load of goals past someone."