New Zealand born Fallon - whose dad was once a youngster at Rotherham - pounced just before half-time to give Swindon their first away win, in the only League game played on FA Cup second round day.
Rotherham without a win in their previous 11 league games, came close to an early breakthrough as they forced Swindon onto the back foot.
Paul Evans smashed in a fierce volley after only three minutes but saw it blocked. Then Lee Williamson produced a testing effort before shots from Martin Butler and Deon Burton were cleared.
A free-kick was curled into the penalty area from Paul McLaren and when it was headed clear Evans pounced but saw his shot saved.
As Rotherham kept up the pressure Williamson's cross broke to Evans and his miss-hit effort found its way back to Williamson whose angled shot was off target.
Swindon had to wait until the 37th minute for their first effort when Hameur Bouazza smashed a free-kick wide and a minute later Bouazza almost squeezed through on goal but was shut out.
And seconds before half-time Fallon pounced to make the all important breakthrough as Swindon punished Rotherham on the break.
Jack Smith's low cross from the right came back out and Neale McDermott drilled in a carbon copy cross that was back heeled in by Fallon from close range.
Rotherham claimed the lion's share of possession as they went hunting for an equaliser but were denied by Swindon's spirited defending.
McLaren produced a testing corner but Colin Murdock's towering header was just over the top.
Swindon keeper Rhys Evans produced a superb save after 65 minutes to preserve his side's advantage, diving full length to hang on to John Mullin's blistering drive.
And then Swindon defended remarkably to deny the home side. A McLaren header was headed off the line by Patrick Collins and a super shot from Burton was brilliantly saved by Evans.