Swindon's Billy Paynter scored the only goal as the League One side edged past Blue Square South opponents Woking.
Paynter rewarded Town's first-half dominance by heading home a corner from Jon-Paul McGovern to put them ahead.
Paynter had already had two chances and Tope Obadeyi had twice been denied by Woking keeper Ross Worner.
Woking's Giuseppe Sole came close with an 18-yard free-kick and despite some pressure in the closing minutes of the game, they could not find an equaliser.
Swindon manager Danny Wilson told BBC Wiltshire:
"We knew what to expect, it was a very, very, very tough and physical game and it certainly didn't surprise us.
"With the opportunities we had we should have had more than the one goal, but the one goal is enough to take us through.
"The back four stood very firm, I thought they were fantastic."
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