Sheffield Wednesday - FA Cup finalists in 1993 - fell at the first hurdle at Swindon's County Ground.
For long periods Wednesday looked the better side but Swindon took full advantage of defensive mistakes to coast into the second round.
Wednesday dominated the first half but had nothing to show for it.
Andy Talbot fired narrowly wide, John Paul McGovern brought a good save from Rhys Evans and a sharply taken free-kick by Steve MacLean was also capably dealt with by Evans under his bar.
Swindon struggled to make any kind of impact but took the lead in the 43rd minute with their first shot on target.
Brain Howard took an in-swinging corner and there was confusion in defence between goalkeeper David Lucas and his team-mates allowing the flag kick to drift in for a bizarre opener.
Almost immediately, Evans made another smart save to deny Lewis McMahon an equaliser and on the resumption a swerving shot from Chris Brunt was held on the line at the second attempt by Evans.
Just as it seemed Wednesday had done enough to draw level they went further behind in the 47th minute.
A long throw on the left by David Duke caused more problems for the defence and after they had failed to clear the ball fell nicely for on loan Steve Jenkins who smashed home a fierce right-foot shot.
Sam Parkin almost added another in the next minute before Glenn Whelan pulled a goal back after drilling a right-foot shot past Evans from 15 yards.
Brunt placed a long range free kick on to the roof of the net before Swindon hit back with two goals in the last seven minutes.
Yet more confusion in the defence, this time caused by Jenkins, led to Duke beating Lucas with a deflected shot from the edge of the area.
Wednesday were now a well beaten side when with five minutes remaining Christian Roberts raced on to a long pass out of defence by Duke to smash home Swindon's fourth.