Swindon were in cruise control in the first half after Aaron Drinan gave them the lead inside two minutes, an advantage Paul Glatzel would extend later in the half.
For all the ease of the first half, Town were made to sweat a lot more after the break, but Princewill Ehibhatiomhan struck before Lewis Shipley pulled one back.
It is four wins on the bounce for Swindon since losing Harry Smith, and they moved top of the table, at least for the time being.
With how well Swindon had performed against Crewe Alexandra last weekend, it was no surprise that even arch-tinkerer Ian Holloway stuck with the same starting line-up. Ollie Palmer and Billy Bodin would have to wait for their first league starts, but they provided plenty of menace off the bench.
Barrow gave Swindon an early scare as Filozofe Mabete headed a corner back to Jack Earing. The midfielder zipped a ball back into the near post, and Connor Ripley had to paw it away.
But inside two minutes, Darren Oldaker was provided with oceans of space to play the ball out to Finley Munroe. He galloped from halfway all the way into the box under minimal pressure and found Drinan. The striker had time to take a touch inside the six-yard box before tapping into the net.
Swindon were being afforded all the time in the world on the ball, and were using it nicely. A measured counterattack had two waves before Tom Nichols found Glatzel in the box. He then found Drinan, who pulled a shot wide from the right side of the box.
Despite the ease they found with the ball, Barrow could have made a game of it. After 21 minutes, Tyler Walker pulled out to the right and found his striker partner, Josh Gordon, at the far post. He found space between two Swindon defenders, but headed wide.
Although there was not much pressure being applied to the ball, with Barrow sitting in a deep 442 block, Swindon were not finding it so easy to get the ball into midfield. They were frequently forced to try and find Glatzel and Drinan over the top without a high degree of success.
Just as they were starting to get frustrated, the play opened up for two. Will Wright headed a long ball back towards Barrow. Glatzel volleyed it straight to Oldaker, who strolled forward and played it back through for Glatzel to tuck home.
There was not much air in the Barrow balloon to start with, but it became a vacuum when the second goal went in. They lethargically traipsed around the pitch as Swindon popped the ball around them, and with a little more desire could have extended their lead.
Oldaker came closest when he picked up the ball on the left and almost jogged into the middle before curling a shot wide of the top corner.
The second half gave no early signs that the winds were changing. Multiple early rampages saw Joe Snowdon and Munroe provided plenty of space to run into, although Swindon did not make the most of the openings.
But the intensity was just slipping away from the Swindon were performance. In the first 15 minutes of the second half, sloppy passes led to Walker heading wide and Gordon having a deflected shot loop behind for a corner.
Holloway was evidently less than pleased and went for his experience after 58 minutes, as Ollie Clarke, Ollie Palmer, and Billy Bodin were all summoned.
This was not having the desired impact as Palmer's header away from a free kick came out to Elliot Newby on the edge of the box. He leathered one first time towards the bottom corner, and Connor Ripley was needed with a fine stop down to his right.
Swindon were still drifting as Gordon slipped at the wrong moment after taking the ball down on the edge of the box. Then Newby was again causing trouble when he curled the ball onto Walker's head for him to nod wide of the target.
But just as things were getting a bit too uncomfortable, Swindon seemed to have the goal to say goodnight. Drinan had moved out to wing-back, and his high cross cleared Palmer, but not Ehibhatiomhan, who arrived to score with his first touch.
Although it was not quite over. A few minutes later, a Barrow shot had Ripley diving, but the ball was deflected straight to Shipley, who diverted it into the far corner to score.
More pressure was applied, but ultimately, Swindon's first-half dominance proved to be too much for the hosts to claw back, and they made it four straight wins across all competitions.
BAFC starting XI: Stanway, Shipley, Raglan, Jackson, Walker, Newby, Earing, Booty, Gordon, Worrall, Barkuizen.
BAFC substitutes: Winterbottom, S. Smith, Cameron, Mahoney, K. Smith.
STFC starting XI: Ripley, Mabete, Wright, Nichols, Glatzel, Wilson-Brown, Kilkenny, Snowdon, Drinan, Munroe, Oldaker.
STFC substitutes: Ward, Clarke, Butterworth, Ehibhatiomhan, Palmer, Bodin, McGregor.