Tranmere led by two goals at the interval and there might have been more against a shaky Swindon defence which let in seven at Nottingham Forest little more than a week ago.
Jamie Cureton pulled one back for the Robins, who had falen behind to Chris Greenacre and Sam Aiston strikes, but it was not enough to save the Robins' from their 15th loss of the season and leaves them rooted in the bottom four.
Yeovil Town's hopes of catching Scunthorpe were hit by a 2-1 home loss to Brentford.
Substitute Alex Rhodes came off the bench at half-time to score the 58th minute goal that gave the Bees victory and lifted Martin Allen's team to second place in the table.
Yeovil were already a goal down. Isaiah Rankin and Lloyd Owusu had proved a real handful and this pair produced the goal with Owusu flicking on a long free-kick from keeper Stuart Nelson and Rankin finished from close range.
Yeovil's leveller in the 25th minute followed a free-kick awarded for a foul that put Amankwaah out of the game.
Nathan Jones' free kick was knocked back to him and when he lobbed to the far post skipper Terry Skiverton was well placed to head in.