United took the lead on 29 minutes when Caolan Lavery seized on a mix-up in the Swindon defence to slot home.
And he turned provider six minutes later as his driven cross was smashed in from close range by Kieron Freeman.
Top-scorer Billy Sharp almost made it 3-0 but narrowly failed to get on the end of Jack O'Connell's teasing centre.
Charlie Colkett reduced the deficit within a minute of the re-start with a long-range shot and United were stunned seven minutes later when Ben Gladwin rifled home an equaliser from the edge of the penalty area.
Swindon's joy was short-lived as the Blades retook the lead on 58 minutes through Jay O'Shea's close-range strike after more poor defending from the hosts.
Paul Coutts sealed the win in stoppage-time from the penalty spot after Samir Carruthers had been fouled by Colkett.
Match report supplied by the Press Association.
Sheffield United strengthened their position at the top of League One with victory over relegation-haunted Swindon at the County Ground.