Swindon went into the half time break with a 1-0 lead thanks to an Andy Gurney free kick from just outside the area with a minute of the first half left.
Earlier in the first half Sam Parkin had also gone close to scoring, whilst Leeds had few chances to score.
Leeds played better in the second half, but still couldn't score, then on 74 minutes Sam Parkin scored in front of the Swindon fans to make it 2-0 after some excellent build up play.
Swindon's 2-0 lead although deserved didn't last and five minutes later Leeds were back in the game with a close range goal to make it 2-1 to Swindon.
Swindon tried to hold on for the remaining 15 minutes, but their cause was not helped with goal keeper Bart Griemink was shown his second yellow card of the game on 87 minutes and sent off after bringing down Leeds Alan Smith on the edge of the area. Rhys Evans took over in the Swindon goal, and had to make a late save to keep Swindon in with a chance.
3 1/2 minutes into the 4 minutes of added time Leeds had a corner, and their goal keeper Paul Robinson ran right up the Evans goal. Robinson managed to head to ball and scored to make the score's level at 2-2 and force the game to go to extra time.
The 30 minutes of extra time passed with Leeds Alan Smith missing their best chance to win the game, Swindon also came close to scoring.
The game then went to the dreaded penalty shoot out. Leeds scored their first penalty, and Sam Parkin scored Swindon's first penalty, then Leeds in the post, and Brain Howard scored for Swindon to make the penalty shoot out 2-1 to Swindon after two penalties each. Leeds and Swindon (Ian Herring) scored the third penalties, then Leeds scored their fouth penalty, but Miglioranzi's penalty was saved to make the score 3-3 after 4 penalties. Leeds scored their final penalty, but Swindon's Andy Gurney who had scored from a free kick in the first half had his final shot of the game saved to put Leeds in the third round of the Carling Cup.
The final score was Leeds 2 Swindon 2 after extra time, and Leeds won 4-3 on penalties to put Swindon out, even though Swindon had much the better game, and remain unbeaten in normal time since the first game of the season.