Crawley twice came from behind to book their place in the first round of the Carling Cup as the new English domestic season got underway at Broadfield.
Luke Moore fired AFC Wimbledon ahead before Hope Akdan levelled seven minutes from the break.
Summer signing Jack Midson restored the Dons' lead early in the second half.
But Sergio Torres quickly equalised before Matt Tubbs' 64th-minute winner earned a meeting with Crystal Palace, despite Akdan's late red card.
The two Football League new boys met in this preliminary round tie to allow Championship side Birmingham City, the holders, to start in the third round because of their Europa League commitments.
Crawley's meeting with Palace, with whom they drew 0-0 with in a pre-season friendly last week, will be played in the week commencing 8 August.
AFC Wimbledon boss Terry Brown told BBC London 94.9:
"As a manager of course I'm disappointed with the result. The performance in certain parts was very good.
"I'm really pleased with the character we showed at the end, going 3-2 down and coming back. But I thought we could have nicked an equaliser.
"If I look a the game as a whole, they deserved to win it. I thought they pressed us very well and stopped us playing."