Kevin Nugent kept faith with the side that earned a battling point at Doncaster and fit-again Alan Tate took a place on the bench at the expense of Kevin Amankwaah.
But the caretaker manager's defence was caught napping in the third minute when they failed to clear the ball and Sharp drove in for his 22nd strike of the season.
There was plenty of fight and endeavour from the Swans, but despite all the possession they rarely troubled Joe Murphy in the visitors' goal.
Too often promising approach play was wasted by a poor final ball and the Swans' best chance of an equaliser came from a multitude of free-kicks they were awarded in various positions just outside the box.
They suffered a blow right on half-time when the bustling Ade Akinfenwa, who had been a constant threat to the visitors, was stretchered off with a suspected broken leg.
Nugent started the second half with a treble substitution with Pawel Abbott replacing the injured Akinfenwa and Tate and Darren Pratley entering the fray for Izzy Iriekpen and Ian Craney.
The second period was much the same as the first with the Swans winning most of the possession but unable to do anything with it.
Andy Robinson brought a flying save from Murphy in the 65th minute but five minutes later the match was as good as over.
Substitute Neil MacKenzie fired in a speculative shot from 30 yards that Willie Gueret could only push into the air leaving Beckford the easy task of putting the ball over the line.
Then the Swans faded badly after that and they could have slipped even further behind but for a smart Gueret stop from Sharp.
A new manager must be appointed as soon as possible to lift the club and prevent them from sliding into mid-table mediocrity.