The visitors tried hard to turn the form book upside down in a terrific second-half performance in which they did everything but score.
It was only a man-of-the-match display by home keeper Murphy that denied them.
Twice he saved brilliantly from striker Ian Henderson after he broke free into the box. Then Murphy turned away a goalbound drive from winger Ritchie Partridge.
And he topped the lot with a tremendous 67th minute penalty save, turning away the spot-kick from midfield man Eugen Bopp after Partridge had been held back in the box by full-back Lee Ridley.
Scunthorpe had opened the scoring in the 17th minute with a super solo effort from striker Beckford, who is on loan from Leeds United.
It was his second goal in four games as he showed neat footwork on the edge of the box before unleashing a left-foot drive that curled beyond the reach of goalkeeper Neil Cutler and into the net off the inside of the far post.
That though was one of the few times that the home side threatened as Rotherham dominated the second period.
The visitors were also hampered when goalkeeper Cutler was stretchered off on the stroke of half-time after a challenge from Richard Hinds.
Another serious injury, this time to Scunthorpe's full-back Cliff Byrne, produced nine minutes of stoppage time at the end of the match.
Rotherham continued to storm forward but were out of luck again when a close-range shot from Henderson rattled a post and stayed out.
It leaves the visitors still anchored at the foot of the table but desperately unlucky not to have taken something from a run now of 11 games without a win.