Howard Pritchard and Andy Rowland both score hat-tricks, as the Town put seven past the sorry Shots.
Colin Bailie nets a late own goal to give Aldershot the lead - the Shots go on to double their lead, winning 2-0 at the County Ground.
Lou Macari pokes home the winner, as the Town come from behind to beat Aldershot.
Two goals to the good - but Fraser Digby's sending off means that Jimmy Quinn has to take his place between the sticks - future Town boss Andy King pulls one back, and the Shots eventually win 3-2 to end the Town's Wembley dream.
The Town win on penalties in the JPT, after Aldershot threaten to embarrass them.
Aldershot look to have got themselves on level terms, but their goal is disallowed - minutes later, a defender puts the ball in his own net to seal victory for Swindon.
Failure to secure the point needed to secure promotion prompts a scathing outburst from Town boss Paolo di Canio, who accuses his players of celebrating too early.