The Iron held a 2-0 lead at half-time having almost conceded in the fourth minute when Michael Timlin's 20-yard power drive bounced down off the bar with Swindon claiming the ball had crossed the line.
The home side had the advantage in the early stages, but as Scunthorpe came more into the game they began to come forward and in the 25th minute Grant McCann's corner was headed off the line by the former Iron loanee Timlin.
When the ball was returned into the goal area Mirfin flicked on for Gary Hooper to bundle the ball over the line.
With the visitors continuing to mount threats Mirfin was guilty of an horrendous challenge on Timlin and with most spectators expecting a dismissal referee Chris Sarginson produced only a yellow card.
It got worse for the home side when Scunthorpe went further ahead six minutes before the break when Hooper provided an excellent ball to enable Henri Lansbury, making his first start for the club, to find an excellent finish past Petr Brezovan for a 2-0 interval lead.
Swindon made changes in defence bringing on teenager Sean Morrison in place of Jean-Francois Lescinel, but it was at the other end where the fireworks started.
Byrne was booked a second time for a foul and dismissed in the 47th minute.
Swindon brought on Anthony McNamee, who quickly became a threat on the flanks. There was more woe for Scunthorpe when Mirfin was also booked a second time and was red-carded to reduce the visitors to nine men.
Although Scunthorpe adopted a defensive formation Timlin reduced the arrears in the 63rd minute, before McNamee's cross was headed into his own goal by Andrew Wright in the 72nd minutes
Hal Robson-Kanu gave Swindon the lead after 82 minutes and three minutes later substitute Lee Peacock made it 4-2.
This was not a game thatthe referee Sarginson will look back on as a vintage performance, as he was very influential in the final outcome.