The hosts never looked back from the moment midfielder Danny Hollands, on loan from Charlton, scored with a deflected shot in the fourth minute.
Raffa de Vita got the second just three minutes later after cutting in from the left and there was no way back for Ronnie Moore's shell-shocked Tranmere.
Andy Williams had time to turn on the edge of the area to score a third after 21 minutes and Matt Ritchie made it four shortly after the half-hour when he was left unmarked at the far post.
Moore made two half-time changes, sending on Donervorn Daniels and Michael Kay but it made little difference.
Six minutes after the break Matt Ritchie found Williams in space to score his second of the evening and only then did Swindon ease up, their job done, with Williams missing the chance of a hat-trick when his penalty was well saved by Owain Fon Williams.
Tranmere stay top, for 24 hours at least, despite the crushing setback but Swindon move up to fifth, a mere two points behind.
