Beckford was one of a number of first team players who were on show, with Sean Gregan, Robbie Blake and Frazer Richardson also playing for 90 minutes, and their performance was watched by Mick McCarthy, whose Wolves team are preparing to face Leeds on Sunday, Adrian Heath and Neil Aspin.
And Vale took the lead 10 minutes before the break when Christian Smith put home a fine individual effort, but Beckford headed home United's equaliser deep into first-half injury time.
Vale pushed for a second goal after the break with a lot of possession but appeared to be heading for a point until substitute Madden scored in the final minute to take maximum points back to Yorkshire.
Reserve team boss Dave Geddis admitted that United had been fortunate to emerge from Vale Park with three points. "We played some decent football at times, but our finishing wasn't fantastic," said Geddis. "We should have been more clinical. "
Whites: Lund, Richardson, Camfield, Hird, Gregan, Hutton (Madden h/t), Gardner (Brown 77), Blake, Beckford, Howson, Bayly.
Unused Subs: Wilberforce, Ameobi, Wilkinson.